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LEMON TECHNOLOGIES AND ADOPTION: MEASUREMENT, THEORY AND EVIDENCE FROM AGRICULTURAL MARKETS IN UGANDA*
TESSA BOLD KAYUKI C. KAIZZI JAKOB SVENSSON
DAVID YANAGIZAWA-DROTT
December 2016
To reduce poverty and food insecurity in Africa requires raising productivity in agriculture. Systematic use of fertilizer and hybrid seed is a pathway to increased productivity, but adoption of these technologies remains low. We investigate whether the quality of agricultural inputs can help explain low take-up. Testing modern products purchased in local markets, we find that 30% of nutrient is missing in fertilizer, and hybrid maize seed is estimated to contain less than 50% authentic seeds. We document that such low quality results in low average returns. If authentic technologies replaced these low-quality products, however, average returns are high. To rationalize the findings, we calibrate a learning model using data from our agricultural trials. Because agricultural yields are noisy, farmers’ ability to learn about quality is limited and this can help explain the low quality equilibrium we observe, but also why the market has not fully collapsed.
* Forthcoming in The Quarterly Journal of Economics. We gratefully acknowledge coeditors Larry Katz and Andrei Shleifer, and four anonymous referees for many valuable comments and suggestions. The authors would also like to thank Aletheia Donald, Frances Nsonzi, Charles Ntale, and Vestal McIntyre for excellent research assistance, and Michael Kremer, Hannes Malmberg, Benjamin Olken, David Strömberg, Tavneet Suri, Christopher Udry and several seminar and conference audiences for comments. Financial support from the Swedish Research Council (421-2013-1524) and International Growth Center is greatly appreciated.
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I. INTRODUCTION
Over the last half century, agriculture in Sub-Saharan Africa has failed to experience any
significant productivity improvements (Evenson and Gollin, 2003). This is broadly viewed as a
central reason why the region has not embarked on a path of sustained economic growth and why
mass poverty is still widespread. Low use of modern, but simple, technologies, including
fertilizers and hybrid seeds, is often suggested as an explanation for why agricultural productivity
has remained stagnant, but why adoption rates are so low still remains somewhat of a mystery
(see reviews in Foster and Rosenzweig, 2010; Jack, 2011, for example).
A number of promising, and potentially interlinked explanations, have been put forward in
the recent literature, including missing markets for risk and credit (Karlan et al., 2014), lack of
knowledge and behavioral constraints (Duflo et al., 2006, 2011), and uncertainty (Suri, 2011). In
this paper we investigate a complementary explanation that takes its starting point in the
technology itself: namely the quality of the technology as provided in the market. This
investigation provides the first large-scale empirical assessment of the prevalence of poor quality
technologies (fertilizer and hybrid seed) in local markets in Africa and the implications this has
on the economic returns to adoption. To this end, we combine data from laboratory tests with
data from researcher-managed agricultural trials. We complement the objectively measured
quality data with information on farmers’ beliefs about the quality of inputs in the market and
their beliefs about the expected yield returns of using either authentic or market based inputs.
We establish that low quality inputs are rife in the local retail markets we surveyed.
Specifically, we find that 30% of nutrient is missing in fertilizer, and hybrid maize seed is
estimated to contain less than 50% authentic seeds. Moreover, we document that such low quality
results in close to zero average rates of return in our baseline specification. If authentic
technologies replaced these low-quality products, however, average returns for smallholder
farmers would be over 80%. Together these results suggest that one reason smallholder farmers
do not adopt fertilizer and hybrid seed is that the technologies available in local markets are
simply of too low quality to be profitable.
We use our data to rationalize the results we document. Specifically, the data show not only
low average fertilizer quality but substantial heterogeneity in quality which is not correlated with
price. This suggests that farmers’ ability to infer quality may be severely limited, since we would
otherwise expect prices to adjust (Shapiro, 1982; Mailath and Samuelson, 2001). To investigate
2
this further, we exploit data from our agricultural trials. The experimental data provide not only
estimates of average yield conditional on quality, but also an estimate of the whole density of
yields, for a given quality. We use these data and calibrate a simple Bayesian learning model to
show that farmers experimenting on small plots will quickly be able to infer that the quality of
fertilizer is low if the level of dilution of the fertilizer is sufficiently high.1 Consistent with this
finding, we find few samples with very low quality in the market place. However, for almost the
full range of sub-standard inputs we observe in the market, we estimate that most farmers in the
model, even after several periods of experimentation, would not gather enough information to
confidently conclude that bad quality is sold, when that is in fact the case. On average, the
Bayesian farmers’ willingness to pay for fertilizers with market quality is also low, although there
will be some farmers who, after observing high yield from relatively low quality inputs in a small
number of experiments, end up with a willingness to pay equal to or above the average market
price. This result can help explain the low, but positive, average adoption rate we observe in the
data. Our findings also help explain why we do not observe sellers selling high quality at a
premium price: the pecuniary incentives to build up and maintain a high quality reputation, given
the beliefs of the farmers we surveyed, simply appear too weak. We argue, however, that by
lifting some of the constraints to adoption that have been highlighted in the recent literature, one
could, through the improved learning environment that would likely follow, create stronger
incentives for a high quality seller to enter the market.
The paper is structured as follows. In Section II we briefly describe the context. Section III
describes the data. Section IV presents the main findings on the quality of the technologies
available in the market. In Section V we estimate the returns to adoption, and in Section VI we
present results on farmers’ beliefs about quality in the market and their expectation of yields
conditional on quality. In Section VII, we rationalize the observed low-quality equilibrium by
developing a parsimonious Bayesian learning model and use data from the agricultural trials to
1 Our modelling set-up is related to other work on technology adoption in agriculture. In Foster and Rosenzweig (1995) and Conley and Udry (2010) farmers learn about the optimal level of fertilizers (with a fixed quality) to be applied. Besley and Case (1994) and Munshi (2004) present models where farmers learn about the expected yield when applying fertilizers (of a fixed quality). Hanna et al. (2014) examine a learning model in which farmers do not pay attention to certain dimensions of the production function. In contrast, the Bayesian farmer here learns about the quality of the technology itself.
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quantify farmers’ ability to learn, and their willingness to pay, from small-scale experimentation.
Section VIII, concludes with a discussion of the implications of our findings.
II. CONTEXT
The agriculture sector in Uganda, as in most countries in the region, is dominated by
smallholder farmers, a majority of whom cultivate less than two hectares. Maize is the most
widely cultivated crop and is grown throughout the country, often on soil with low fertility.2
Data on smallholder farmers’ technology use (fertilizer and hybrid seeds) in Africa are
sketchy. The World Development Indicators, using data collected by FAO, report average
fertilizer consumption (kilograms per hectare of arable land) for a large set of Sub-Saharan
African countries. However, since large scale commercial farms and agricultural producers
consume a large fraction of the total, these averages typically do not provide an accurate measure
of smallholder farmers’ use.3
Nationally representative household surveys with a focus on agriculture exist for some
countries. The LSMS Integrated Surveys on Agriculture program, for example, has collected
panel data for eight Sub-Saharan African countries, including Uganda. Table A.1 extends and
updates Sheahan and Barrett’s (2014) estimates of overall national fertilizer and improved seed
use statistics using the latest rounds of LSMS data. Based on data for 2012/2013, we estimate that
7% of cultivating households in Uganda, and almost one in ten households growing maize, used
some type of fertilizer in the last year. 22% of cultivating farmers report planting improved seeds
on at least one of their plots.4 There are large variations in input use across Uganda’s four
regions, with very low usage of fertilizer and improved seed in the Northern region, while 13% of
cultivating maize growing households report using fertilizers, and 27% report using improved
seeds, in the main maize growing region.
Adoption rates are higher for fertilizers, but more similar for improved seeds, in the other
seven countries surveyed by the LSMS (see Table A.1), with the share of households using some
2 Declining soil fertility has been highlighted as a key concern in Sub-Saharan Africa, including Uganda (Sanchez, 2002; Nkonya, Kaizzi, Pender, 2005). 3 For example, average fertilizer consumption in Mozambique was approximately four times higher than in Uganda in 2013 (World Bank, 2016), but only 3% of imported fertilizer was used for food crops, and only a fraction of this was used by smallholder farmers. 50% of the imported fertilizer was used by a multinational tobacco producer (World Bank, 2012). 4 Improved seeds are either open pollinated variety seeds (OPV) or hybrid seeds.
4
inorganic fertilizers varying from 15% (in Tanzania) to 78% (in Malawi), and the share of
households using some improved seeds varying from 15% (in Niger) to 49% (in Malawi).
Most Sub-Saharan African countries, as is the case also for Uganda, import fertilizers but a
significant fraction of the hybrid seeds in the market are produced domestically. In Uganda, large
commercial farms and agricultural producers source fertilizers directly through international
sources, or through one of the approximately ten importers, many of whom also act as domestic
distributors or wholesalers, and buy hybrid seeds directly from national seed companies or from
importers linked to international seed producers (IFDC, 2014). There is also a larger set of
wholesalers/retailers in the market, which do not import inputs themselves, from which local
agro-input retail shops typically source.
Ugandan supply costs mirror those documented for farmers in Kenya and Tanzania, but
Ugandan farmers face higher transport costs due to longer distances and border-related
constraints (IFDC, 2014). In addition, and unlike most countries on the continent, Uganda does
not have a national fertilizer subsidy program, which is likely one important explanation for the
relatively low average fertilizer use.5 Uganda also differs from several other African countries in
that there is no state participation in import and distribution of fertilizers and hybrid seeds.
In local retail stores, hybrid seeds and fertilizer are usually sold in smaller packages which
the retailer has repacked from larger bags. Most fertilizers are sold under their generic name
(urea, DAP, NKP for example) while hybrid seeds (when in large bags) typically are branded
with names specifying the seed producer and type of seed.
The concerns about poor quality inputs in the agricultural sector is not a new one and not
specific to Uganda. In fact, addressing poor quality inputs through the strengthening of the
regulatory enforcement capacity and the capacity for quality assurance was listed as one of the
main policy recommendations in a recent USAID funded review of fertilizer markets in 12 Sub-
Saharan African countries (IFDC, 2015).
Low quality inputs could be due to a multitude of factors, including adulteration, poor
storage and inappropriate handling procedures. Moreover, quality deterioration could manifest at
different points in the supply chain. There is anecdotal evidence and news reports from many
African countries about adulteration of both seeds, fertilizers and other agro-inputs such as
5 Many African countries have a subsidy program for fertilizer and some also for hybrid seeds. There are large differences in how these programs work and the extent of the subsidy across countries. The most generous program is in Malawi, where participating farmers receive a subsidy up to 90% for both fertilizers and seeds (IFDC, 2013).
5
pesticides, at different parts of the supply chain, including the importation of diluted inputs and
the bulking out of fertilizer or dyeing simple grain to look like hybrid seeds by wholesalers.
However, while news reports across the region have primarily focused on adulteration scandals at
the higher end of the supply chain, anecdotal evidence suggests that adulteration also takes place
at the retail level, where larger bags are repacked into smaller ones. The repacking and the open
air storage of larger bags in retail stores can also lead to dilution of key nutrients in fertilizer and
lower the quality of hybrid seeds.
III. DATA AND MEASUREMENT
We investigate the quality of one of the most popular high-yield variety maize seed in the
Ugandan market, as well as a generic nitrogen-based fertilizer (urea). Nitrogen has been shown to
be the main limiting nutritional component to maize growth in Uganda (Kaizzi et al., 2012).
To measure the quality of the technologies in the market, we combine data on the nitrogen
content of fertilizer from retail shops and experimental yield data from our own agricultural trials.
At 129 randomly sampled local retail shops in two of the main maize-growing regions of
Uganda, we purchased 369 samples of urea fertilizer (‘retail fertilizer’), and at 30 such shops we
purchased 30 samples of branded hybrid seed of the predetermined type (‘retail hybrid seed’),
using a mystery shopper approach (see online appendix for details). We also purchased urea and
hybrid seed in bulk directly from one of the main wholesalers for urea (‘authentic fertilizer’) and
the seed company producing the branded seed (‘authentic hybrid seed’). Finally, we purchased
traditional farmer seed from a random sample of 80 small-scale maize farmers living around the
trading centers where hybrid seed were purchased.
Each retail fertilizer sample was tested three times for the content of nitrogen (N) using the
Kjeldahl method (Anderson and Ingram, 1993) at the Kawanda Agricultural Research Institute
laboratory. We used the mean of these tests to determine the quality of a sample. Authentic urea
should contain 46 percent nitrogen (%N) and we confirmed this to be the case in our “authentic”
sample.
Researcher-managed agricultural trials at five of the National Agricultural Research
Laboratories' research stations across Uganda were used to determine the yield responses of
fertilizer and to estimate the quality of hybrid seed sold in retail markets. Authentic urea was
diluted by proportionately adding acid-washed sand to get urea samples with 75% of stated N
(approximately 34%N), 50% of stated N (approximately 23%N), and 25% of stated N
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(approximately 11%N). Together with authentic urea (46%N) and no urea, this yields five
fertilizer treatments (N = 46%; N=34%; N=23%; N=11%; N =0%). We combined the five
fertilizer treatments with the three seed treatments (authentic hybrid seed, retail hybrid seed, and
farmer seed) to yield 15 possible seed-fertilizer quality combinations that were randomly
assigned six 30m² plots each at each of the five experimental sites. In total, each treatment
combination was grown 30 times and yield data was collected from 450 plots.
The crop management and data collection protocol (see online appendix for details) followed
the methodology outlined in Kaizzi et al. (2012). All five sites were managed by the research
team, and the staff assigned to implement the trial protocol were blinded to the treatment status of
the plots. We planted two maize seeds per hill with a spacing of 30×75 cm between hills, for a
total of 105 hills per plot. We applied fertilizer at 108 kilograms per hectare (which corresponds
to the official recommendation of 50kg N/ha for authentic urea) in two splits: half at planting by
broadcasting and immediately incorporating into the soil and half later at tasselling top dress. In
harvesting, we excluded the outer perimeter of the plot, and we oven-dried the grains to correct
for moisture.
Unlike the content quality of fertilizers, which can be tested directly in a laboratory, we infer
the quality of retail hybrid seeds by focusing on their yield response. Intuitively, we assess the
quality by assuming the following: if a bag of farmer seed yields 𝑋𝑋 tons of maize, a bag of
authentic hybrid seed yields 𝑌𝑌 tons of maize and a bag of retail hybrid seed yields 𝛼𝛼𝑋𝑋 + (1 − 𝛼𝛼)𝑌𝑌
tons of maize, then the bag of retail hybrid seed is of the same quality as a bag of authentic hybrid
seed that is diluted with 𝛼𝛼% farmer seed.
More formally, we first match the experimental yield data for the three types of seed by site,
block and nitrogen content of the fertilizer applied. Then we construct a new variable in each of
these strata, which is the weighted sum of the average maize yield on the plots growing farmer
seed in stratum s and the average maize yield on the plots growing authentic hybrid seed in
stratum s: 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚 = 𝛼𝛼𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑚𝑚𝑓𝑓𝑓𝑓 + (1 − 𝛼𝛼)𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑓𝑓𝑎𝑎𝑎𝑎ℎ𝑓𝑓𝑒𝑒𝑎𝑎𝑚𝑚𝑒𝑒. Third, we calculate the first four
central moments of this new variable and of the distribution of yields on plots growing retail
hybrid seed – the latter also averaged over the plots in each stratum. Finally, we infer the most
likely level of dilution by finding 𝛼𝛼 that minimizes the squared weighted difference between the
simulated moments and the data moments (see online appendix for details).
7
We complement the data on the quality of the technology with household survey data,
administered to 312 small-scale farmers (farmers with farms of two hectares or less) residing
around the trading centers visited as part of the fertilizer quality study. The household survey
collected detailed data on farmers’ agricultural practices, including input use and market
interactions, and their expectations about the quality of and yield return to fertilizers (see online
appendix for details).
IV. THE QUALITY OF THE TECHNOLOGY
As reported in Table I, and illustrated in Figure I, on average, retail fertilizer contained 31%
less nutrient than authentic fertilizer, or 31.8% N per kilogram (95% CI: 31.1-32.6). Defining
fertilizer dilution in sample 𝑗𝑗, 𝑌𝑌𝑗𝑗, as 𝑌𝑌𝑗𝑗 = �46 − %𝑁𝑁𝑗𝑗�/46, we find no fully authentic fertilizers
and less than 1% with a dilution level (𝑌𝑌𝑗𝑗) less than 10%. We also observe very few highly
diluted samples (4% of the samples are diluted by more than 50%). In other words, the large
majority of samples (95%) have low to moderate dilution levels (ranging from 10% to 50%).6
Figure II shows that while there was substantial variation in quality across samples, prices
were homogenous.
Figure III links quality of the inputs to yields, and shows that shortfalls in quality reduce
yields substantially. For example, average yield is approximately 40% higher when using
authentic inputs (fertilizer and hybrid seeds) than when using inputs with average retail quality.
Columns (1)-(3) in Table II report estimates of linear regressions of yield on nitrogen
content (%N) when planting either farmer seed, retail hybrid seed, or authentic hybrid seed. A
reduction of nitrogen by 1 percentage point when planting traditional farmer seed leads to a
significant yield loss of 49 kilograms per hectare (P<0.001, t test). The loss due to poor quality is
even higher when planting retail hybrid seed (57 kg/ha, P<0.001, t test) and the highest when
planting authentic hybrid seed (65 kg/ha, P<0.001, t test). For the fertilizer ranges considered
here, the quality of the technology is approximately linearly related to yield as graphically
illustrated in Figure IV, using a nonparametric Fan local regression method.7
6 In a follow-up study (see online appendix for details) we show that dilution of fertilizers is not specific to urea. A test of 126 samples of DAP – a multinutrient fertilizer with nitrogen and phosphorus as the main nutrients – shows an average dilution level of 25.9%, ranging from essentially 0 to 91% dilution. 7 It is well established that at higher levels of fertilizer application the marginal yield return to (nitrogen based) fertilizers is falling in the amount of fertilizer applied (see for example Duflo, Kremer, and Robinson, 2008; Kaizzi et
8
The results of the simulated moments estimation on retail seed quality are presented in Table
III. The simulated method of moments estimate for 𝛼𝛼 is 0.52 (95% CI: 0.30-0.74). From this we
conclude that the average quality of a bag of retail hybrid seed is roughly the same as the quality
of a bag mixed 50-50 with farmer seed and authentic hybrid seed. Figure A.1, in the appendix,
plots the cumulative distribution function (CDF) of retail hybrid seeds and of the distribution
generated by mixing farmer (55%) and authentic hybrid seeds (45%). The two curves lie almost
on top of each other and a Kolmogorov-Smirnov test confirms that we cannot reject the null
hypothesis that the two distributions are equal (p-value=0.90).
V. THE ECONOMIC RETURNS TO TECHNOLOGY
Having established that modern technologies available in local retail markets are of poor and
heterogeneous quality, we examine how quality affects the returns to adoption of retail hybrid
seed and retail fertilizer. The unit of observation for these calculations is a retail fertilizer sample.
The net return of a fertilizer sample j with nitrogen content 𝑛𝑛𝑗𝑗 percent Nitrogen (%N)
applied to retail hybrid seed is the difference between the revenue from planting retail hybrid
seed with retail fertilizer – less the direct and additional labor costs associated with the inputs –
and the revenue from planting traditional seed with no fertilizer. The rate of return of adopting
fertilizer and hybrid seed is given by dividing the net return by the total cost of adoption. A
fertilizer sample is deemed profitable if its rate of return is greater zero.
Predicted yield for a given seed type and fertilizer quality can be derived from Table II.
Specifically, let 𝑠𝑠𝑘𝑘 denote seed type, with 𝑠𝑠1 being farmer seed, 𝑠𝑠2 being retail hybrid seed, and
𝑠𝑠3 being authentic hybrid seed. The predicted yield of a fertilizer sample with nitrogen content 𝑛𝑛𝑗𝑗
%N using seed type 𝑠𝑠𝑘𝑘 is 𝑦𝑦��𝑛𝑛𝑗𝑗 , 𝑠𝑠𝑘𝑘� = 𝛼𝛼�𝑘𝑘 + �̂�𝛽𝑘𝑘 × 𝑛𝑛𝑗𝑗 where the subscript k on the estimated
coefficients refers to the column number in Table II.
The predicted net return (NR) of a fertilizer sample j with nitrogen content 𝑛𝑛𝑗𝑗 %N, using
retail hybrid seed, is calculated as
(1) 𝑁𝑁𝑁𝑁�𝑛𝑛𝑗𝑗 , 𝑠𝑠2� = 𝑝𝑝𝑚𝑚𝑦𝑦��𝑛𝑛𝑗𝑗 , 𝑠𝑠2� − 𝑐𝑐𝑗𝑗𝑓𝑓 − 𝑐𝑐𝑠𝑠 − 𝑌𝑌𝑓𝑓𝑠𝑠 − 𝑝𝑝𝑚𝑚𝑦𝑦�(0, 𝑠𝑠1) ,
where 𝑝𝑝𝑚𝑚 denotes the market price of maize (per metric tons), 𝑐𝑐𝑗𝑗𝑓𝑓 and 𝑐𝑐𝑠𝑠 are the costs of fertilizer
and seed per hectare, and 𝑌𝑌𝑓𝑓𝑠𝑠 is the additional labor cost per hectare of land; i.e., the
al., 2012; Wortmann, et al., 2011). Here we consider the lower end of the relationship between applied nitrogen and yield for which there is little experimental evidence.
9
complementary input responses due to adoption of hybrid seeds and fertilizers. 𝑝𝑝𝑚𝑚𝑦𝑦��𝑛𝑛𝑗𝑗 , 𝑠𝑠2� is
the predicted revenue per hectare of land, using the results in Table II, column (2), to predict
𝑦𝑦��𝑛𝑛𝑗𝑗 , 𝑠𝑠2�. 𝑝𝑝𝑚𝑚𝑦𝑦�(0, 𝑠𝑠1) is the revenue from traditional farming (no hybrid seed or fertilizer), where
the predicted yield is estimated from Table II, column (1).
To calculate the predicted NR for authentic inputs, we replace 𝑛𝑛𝑗𝑗 with 𝑛𝑛 = 46 and 𝑠𝑠2 with 𝑠𝑠3
in equation (1). Note that the variation in NRs for inputs bought in local markets is driven by
variation in nitrogen content (𝑛𝑛𝑗𝑗), and thus expected yield, and the cost of the fertilizer (𝑐𝑐𝑗𝑗𝑓𝑓),
while the variation in NRs for authentic inputs is driven by differences in costs only.
To estimate the net returns we need data on the output price (𝑝𝑝𝑚𝑚), input costs (𝑐𝑐𝑗𝑗𝑓𝑓, 𝑐𝑐𝑠𝑠), and
the cost of complementary labor inputs (𝑌𝑌𝑓𝑓𝑠𝑠).
The market price for maize per hectare (𝑝𝑝𝑚𝑚) is estimated from the farmer survey where we
collected information on the value and amount of harvest sold in the last season. From this we
derive the price each farmer received. Since the reported output price is strongly left-skewed, we
used the median (UGX 500,000 or ~$170 per metric tons) rather than the mean price.8
The price of each fertilizer sample and the average (and the median) price for the hybrid
seed were collected as part of the covert shopper surveys. The costs of fertilizer and seed, 𝑐𝑐𝑗𝑗𝑓𝑓 and
𝑐𝑐𝑠𝑠, are then calculated assuming that inputs were applied using the officially recommended
amounts per hectare.
Estimating the complementary labor response due to adoption is more problematic, as this
choice is obviously endogenous. As a reference, Beaman et al. (2013) use an experimental design
to estimate the change in complementary input use, including family and hired labor, in response
to free provision of fertilizers. They do not observe any change in the amount of family labor
used, but an increase in hired labor, and estimate that the total complementary input expenses
(excluding fertilizers) account for 26% of total input expenses (including the cost of fertilizers
used) for the treatment group receiving the full fertilizer treatment.
8 The market price for maize varies over the season (see, for example, Burke, 2014). We did not collect data on the timing of the sale. However, due to inadequate on-farm storage, most smallholders are forced to sell their produce at harvest when prices are considerably lower. The estimated farm-gate price of UGX 500/kg is consistent with other data. For example, the Famine Early Warning Systems Network report retail prices of maize in one of the main markets in the Western region of Uganda. At the time of harvest in 2013, the retail price was UGX 600/kg. Since this is the retail price in one of the larger market centers, it provides an upper-bound of the average farm-gate price.
10
Table IV reports the results from regressing family labor and expenses on hired labor on
fertilizer and hybrid seed application, using data from the small-holder farmers we surveyed. In
our sample, 21% of the farmers use some type of fertilizer and improved maize seeds (OPV or
hybrid seeds).9 As in Beaman et al. (2013), adoption of improved seeds and/or fertilizers is not
associated with a significant change in the amount of family labor applied, but increased
expenses on hired labor. Our non-experimental estimates, evaluated at the mean of fertilizer and
hybrid seed costs (𝑐𝑐𝑗𝑗𝑓𝑓, 𝑐𝑐𝑠𝑠), column (3), imply that the complementary expenses for hired labor
(𝑌𝑌𝑓𝑓𝑠𝑠) account for 32% of the total input expenses (𝑐𝑐𝑗𝑗𝑓𝑓 + 𝑐𝑐𝑠𝑠 + 𝑌𝑌𝑓𝑓𝑠𝑠) for farmers using fertilizers and
improved seeds. While these estimates are close to Beaman et al.’s (2013) experimental
estimates, they are not causal estimates, so to check the robustness of the findings we also impute
rate of returns assuming the complementary labor expenses are 25% or 50% less than those
reported in Table IV.
Low quality of inputs in the market reduces the economic returns to adoption substantially.
As Table V, Panel A, shows, using retail fertilizer and retail hybrid seed yields approximately
very low returns on average (mean r = 6.5% and median r = 10.8%). In contrast, if authentic
technologies were sold in local retail stores, the mean and median rate of return would be close to
80%. While 65.6% of the fertilizer samples bought in local markets yield positive returns, only
8.9% yield a return above 25% and none over 50%; two thresholds that are likely to be more
relevant given market interest rates of 20-25%. If all samples had been authentic, 99% of the
samples would have yielded a return above 70%.10
In Panel B, Table V, we re-estimate the returns assuming the costs of the complementary
inputs are 25% lower than in the baseline scenario reported in Panel A, and in Panel C, we report
rate of returns of adoption assuming the costs of the complementary inputs are 50% lower. 25%
lower costs of complementary inputs imply the same cost share, 𝑌𝑌𝑓𝑓𝑠𝑠/(𝑐𝑐𝑓𝑓 + 𝑐𝑐𝑠𝑠 + 𝑌𝑌𝑓𝑓𝑠𝑠), on average,
as in Beaman et al (2013); i.e., 26%, while 50% lower expenses on complementary inputs implies
9 In the research managed trials, urea was used both at planting and for top dressing. It is not uncommon, however, for farmers using fertilizers to use different types of fertilizers at planting and for top dressing. It is therefore more accurate here to use a more aggregate measure of fertilizer use, rather than adoption of a specific type of fertilizer. 10 For single nutrient fertilizers, like urea, given observed dilution levels, the rate of returns would initially tend to increase if farmers use more than the recommended dosage. Overdosing, however, may be less beneficial when applying a multinutrient fertilizers (as the relative magnitudes of the main nutrients matter and diluted multinutrient fertilizer may not have the same relative amounts of the main nutrients as authentic fertilizers), and would not be a viable option for diluted seeds.
11
that the complementary inputs (here hired labor) accounts for less than one-fifth of the total
expenses for adoption.
With 25% lower complementary input expenses (Panel B), the mean rate of return of inputs
purchased in local markets is 15.8% as compared to 99.6% had these inputs been of authentic
quality. 37.1% of the samples bought in local markets would yield a return above 25%, but a
mere 1.1% would yield a return above 50%. With 50% lower complementary input expenses,
more than half of the samples yield a return above 25% but still only 7.9% yield a return above
50%. As a comparison, for authentic technologies, almost all yield a return over 100%.
Our results are also robust along a number of other dimensions. The economic returns
reported in Table V were derived from the experiments run on researcher managed agricultural
stations. The experimental fields were chosen to mimic the agricultural conditions faced by many
smallholder farmers in Africa – and soil tests confirmed that that was indeed the case.11 It is still
likely, however, that the yields, and thus the returns, we estimate are higher than most small-scale
farmers would achieve as the crop management (planting, weeding, harvesting, etc.) followed
recommended practice and the procedures were homogenously applied across all plots. Many
farmers, but to a varying degree, do not consistently follow these recommended guidelines. An
advantage of our approach is that the variation across plots, and mean outcomes, are not driven
by farmer-specific factors. We exploit that variation in Section VII when we try to rationalize the
observed equilibrium in the market. Importantly, it also helps us to interpret the findings we
report in Table V: the estimates provide upper bounds – both for market and authentic
technologies – on the return to adoption; i.e., we estimate the returns that a smallholder farmer
with up-to-date knowledge about crop management should be able to achieve.
Poor crop management would lower yields and thus returns and would therefore make
adoption of inputs bought in local markets even less likely to be profitable.12 To illustrate the
effects, assume yields are 𝜑𝜑𝑦𝑦��𝑛𝑛𝑗𝑗 , 𝑠𝑠𝑘𝑘�, where 𝜑𝜑 > 0. Figure A.2, in the online appendix, plots the
mean rate of returns for retail and authentic technologies for different values of 𝜑𝜑. As an
11 See online appendix, section A.2 for details. 12 We estimate that average yield for small scale maize farmers using traditional technologies (traditional seeds and no fertilizers) in 2013, using data from the 2013/2014 LSMS data for Uganda, was 1.57 metric ton per hectare, or 14% lower yield (95% CI 4%-29%) than what we estimate in the research managed trials with traditional seeds and no fertilizer (see Table A.2). Average yearly yield varies over time, although not strikingly so at the national level where average yield varied between 1.3-1.6 tons per hectare over the period 2009-2013. Average maize yield for the sample of smallholder farmers surveyed here (also in 2013 and using traditional techniques) was 1.4 metric ton per hectare, or 22% lower yield than in the research managed trials.
12
example, if estimated yields are 20% lower (𝜑𝜑 = 0.80) than in the baseline scenario reported in
Table V, Panel A, the mean return is -15% for fertilizer samples bought in local markets, while
the rate of returns for authentic technologies is approximately 50%.
We estimate rates of return based on data for one season. The broad spatial variation in the
data (we use data from five agricultural stations spanning three regions) likely relaxes some
concerns about the generalizability of the estimates. However, as small-scale agriculture in Africa
largely relies on rain-fed irrigation, yield is a function of weather realizations which vary over
time (see Rosenzweig and Udry, 2016). Differences in yield are also likely to map into
differences in net income (value of output minus cost of inputs and hired labor) and relatively
small changes in yield can result in relatively large differences in net income returns.13 Here,
however, we focus on rates of return, defined as the difference between net income and revenues
from traditional farming, expressed as a share of the total costs of the investment. To the extent
that yields and revenues from farming using both traditional and modern technologies vary over
time as a function of weather realizations, the difference between them will net out some of time
series variation due to weather shocks. More importantly, we focus on the difference between
rates of return using technologies from local markets versus authentic technologies, both of
which are functions of weather realizations. In fact, if we approximate the relationship between
the state of nature and yields (or revenue) with the linear function 𝜑𝜑𝑝𝑝𝑚𝑚𝑦𝑦��𝑛𝑛𝑗𝑗 , 𝑠𝑠𝑘𝑘�, where 𝜑𝜑
represents the state of nature, Figure A.2, also illustrates the impact of different weather
realizations. An adverse weather shock resulting in revenues from farming, independent of
technology choice, by say 20%, lowers the mean rate of return for technologies in the market
from 7% to -15% and lowers the mean rate of return for authentic technologies from 84% to
48%. A positive weather shock leading to an increase in revenue by 20% raises the rate from 7%
to 28% and 84% to 120% for technologies in the market and authentic technologies, respectively.
In both cases there are large differences in rates of returns from using technologies available in
local markets versus authentic technologies.
Finally, it is possible that the labor costs when adopting authentic technologies, at harvest,
are higher than the labor costs when using sub-standard inputs, simply because labor costs are a
function of yields. Assuming, for small-scale farming, that approximately a third of all labor costs
are incurred at harvest, consistent with the findings reported in, for example, Suri (2011), and
13 Note that the state of nature (weather realization) may also affect prices (for outputs and inputs).
13
assuming further that our estimate of 𝑌𝑌𝑓𝑓𝑠𝑠captures the average total complementary labor cost of
adoption of inputs from the market, then for a farmer using inputs with average market quality
(𝑛𝑛�, 𝑠𝑠2), labor cost at harvest, per metric ton per hectare, is 𝑌𝑌𝑓𝑓𝑠𝑠/3𝑦𝑦�(𝑛𝑛�, 𝑠𝑠2). If costs are linear in
yield, the (labor) costs incurred at harvest when using authentic inputs is then simply 𝑦𝑦�(46, 𝑠𝑠3) ×
𝑌𝑌𝑓𝑓𝑠𝑠/3𝑦𝑦�(𝑛𝑛�, 𝑠𝑠2). This increase in costs, however, has only a modest impact on the rate of return.
Compared with the baseline scenario reported in Panel A, Table V, the average rate of return of
adoption with authentic inputs goes down from 84% to 77% and all fertilizer samples continue to
yield a rate of returns over 60%.
VI. FARMERS’ EXPECTATIONS
Can poor quality of fertilizer and seeds and low rates of return help explain why farmers do
not adopt modern inputs? For that to be the case, it ought to be the case that (i) farmers expect
that technologies available in the market are of poor quality, and (ii) that farmers expect that there
is a positive relationship between quality of inputs and yields. We turn to these issues next.
A farmer (household) survey was administered to a sample of farmers at the end of the
second season of 2013. For each trading center visited as part of the 2014 fertilizer study, 10
farmers within a 5-kilometer radius from the trading center and 10 farmers in 5–10 kilometer
distance from the trading center were surveyed, using a two-stage sampling strategy (see online
appendix for details). The objective of the survey was to collect detailed information from small-
scale maize farmers on their agricultural practices and their expectations about the quality of and
economic return to fertilizers. In total, information was collected from 312 smallholder farmers.
The subjective expectations module was designed to elicit a farmer’s probability distribution
over yield generated by growing maize on their land either (a) without using fertilizer, or (b) by
applying the recommended amount of urea using fertilizer bought from the nearest shop, or (c) by
applying the recommended amount of urea using fertilizer of the best official quality.
Specifically, farmers were first asked to give an estimate of the range of the distribution. The
enumerator then calculated three evenly spaced mass points between the minimum and the
maximum stated by the farmer. For each elicitation, farmers were given 10 beans and instructed
to place the beans on a plate describing the chance that the event in question would be lower or
equal than this number. We also collected data on farmers’ beliefs about the nitrogen content of
fertilizers in the nearest local shop by asking the respondent to assess the quality of fertilizer on a
14
scale of 1 to 10, where 0 means there is no nitrogen, 5 means that half of the official nitrogen is
there, and 10 is the best possible quality.14
Figure V shows the histogram of farmers’ beliefs about the nitrogen content of fertilizer in
their nearest shop. On average, farmers expect fertilizer bought in the market place to contain
38% less nutrient, equivalent to a nitrogen shortfall of 17.6 percentage points (Table VI). That is,
expectations are on average in line with the results we obtained from the fertilizer samples tested
(see Table I). There is substantial variation, however, even among households close to the same
trading center. Taken together, the results suggest that while farmers as a group predict average
quality relatively well, individual farmers’ ability to infer quality appear more limited.
In Table III, column (4), we report a linear regression of a farmer’s expectation of yields on
her expectation of nitrogen content (%N) in fertilizers bought in the nearest shop, where the latter
has been rescaled to range from 0 to 46%. As evident, there is a strong correlation between the
expected quality of the fertilizer and expected yield. Moreover, the estimated return to nitrogen
based on the farmer’s expectations is similar to the estimates from the experimental plots.
Figure VI puts the two findings together – farmers expect fertilizers in the market to be of
low quality and lower quality is expected to result in lower yield – by plotting the CDF of
farmers’ expectations of yields conditional on technology choice and source of the technology.
The CDF of expected yield using authentic fertilizers is strongly shifted to the right of the CDF of
farmers’ expectations of yields using market quality fertilizer, which in turn lies to the right of the
CDF without fertilizers. A Kolmogorov-Smirnov test rejects the equality of the three distributions
at the 1% level.
VII. RATIONALIZING THE EQUILIBRIUM: LEARNING ABOUT QUALITY
We have shown that poor quality inputs are the norm in the retail markets we surveyed –
spanning two of the main maize-growing regions of Uganda – and that only a small share of the
fertilizers we observe in the market appear profitable. In this section we start to rationalize the
market equilibrium by zeroing in on one key determinant of the equilibrium – farmers’ ability to
learn about quality.
14 See Delavande, Giné, and McKenzie (2011) for a review and analysis of subjective expectations data from developing countries. Despite our attempt to minimize measurement errors, these data should be interpreted with caution since we do not know if the respondents fully understood the key concepts.
15
Fertilizers and hybrid seeds are experience goods; i.e., farmers typically observe neither the
quality of the technology nor the additional output their adoption would yield before purchasing
them. In largely unregulated and unmonitored markets for such goods, a retailer’s incentive to
provide high-quality goods hinges crucially on the buyers’ ability to learn about quality after
using it (Shapiro, 1982; Mailath and Samuelson, 2001).
In assessing the quality of the inputs after use – based on yields after adoption – farmers, and
especially smallholder farmers, face a difficult inference problem. Yields, even holding farming
practice and quality of the inputs constant, vary due to a number of factors that are mostly
unobservable to the farmer, including the fertility status of the soils and the inherent variability of
seeds. Thus, a farmer must disentangle the quality of inputs from a noisy yield signal.
Figure VII illustrates the inference problem by plotting the density of yields for three quality
combinations– authentic inputs, inputs with mean market quality, and inputs with the lowest
quality – using data from the researcher-managed agricultural trials. Even holding quality and
agricultural practice constant, yield varies substantially across plots.
The results presented so far provide indirect evidence of the learning environment. Low
quality is the norm in the market, however, the nutrient content in fertilizers is not zero and the
market has not collapsed, suggesting that farmers do learn about quality to some extent. At the
same time, the variation in quality we observe appears uncorrelated with price, suggesting that
farmers’ ability to infer quality is far from perfect, otherwise one would expect prices to adjust.
We now present a simple learning model, which we calibrate using data from the researcher-
managed agricultural trials, to calculate a Bayesian farmer’s confidence that the fertilizer she is
experimenting with is profitable and the resulting willingness to pay for it. We use the model to
answer two questions: (1) What range of quality levels would one expect to find in the market
given farmer’s (limited) ability to learn about the quality of inputs? In other words, can learning
in a noisy environment explain why the market looks like it does? (2) Would a seller selling
authentic fertilizer be able to build up a reputation for doing so both under the status quo and
when additional constraints are lifted?
VII.A. A Model of Learning About Quality
16
Consider a farmer who wants to adopt fertilizer and starts experimenting with it on a small
plot.15 The farmer knows that fertilizer of sufficiently high quality, say with a rate of dilution 𝜃𝜃 <
𝜃𝜃∗, where 𝜃𝜃∗ is the threshold level, is profitable. However, the farmer cannot directly observe the
quality of the fertilizer in the market; i.e., the dilution level 𝜃𝜃 ∈ [0,1] is unknown. The farmer
must therefore infer quality based on the yields on her plot.
The farmer knows that the systematic relationship between yield (𝑦𝑦) and the quality of inputs
is given by
(2) 𝑦𝑦 = 𝑔𝑔(𝜃𝜃) .
Further, the farmer has some prior belief about the distribution of fertilizer quality on the market
Π(𝜃𝜃) (with density 𝜋𝜋(𝜃𝜃)).16
In period (or on plot) 𝑡𝑡 = 1, a farmer experiments with fertilizer with an unobserved dilution
level 𝜃𝜃𝑎𝑎 = 𝜃𝜃�𝑎𝑎 randomly drawn from a distribution 𝐹𝐹(𝜃𝜃), and receives a private signal 𝜔𝜔𝑎𝑎 about 𝑦𝑦,
after each experimentation (harvest), given by
(3) 𝜔𝜔𝑎𝑎 = 𝑔𝑔�𝜃𝜃�𝑎𝑎� + 𝜀𝜀𝑎𝑎
where 𝜀𝜀𝑎𝑎~𝑁𝑁(0,𝜎𝜎𝜀𝜀2) is a noise term that is unobserved but whose distribution is known to the
farmer. Note that 𝜀𝜀𝑎𝑎 is assumed not to be a function of the unknown input quality.
Observing a signal 𝜔𝜔1, a Bayesian farmer will update his belief; i.e., the density of the
distribution over 𝜃𝜃, at any point 𝜃𝜃. By Bayes rule the updated posterior density is
(4) 𝜋𝜋(𝜃𝜃|𝜔𝜔1) =𝑓𝑓(𝜔𝜔1|𝜃𝜃)𝜋𝜋(𝜃𝜃)
∫ 𝑓𝑓(𝜔𝜔1|𝜃𝜃)𝜋𝜋(𝜃𝜃)𝑌𝑌𝜃𝜃10
,
where 𝑓𝑓(⋅ |𝜃𝜃) is the distribution of the signal conditional on the farmer’s belief about quality.
Iterating on this expression, we can write the density of dilution level 𝜃𝜃 after experimenting for 𝑡𝑡
rounds (or on 𝑡𝑡 plots) as:
15 The assumption that the farmer starts experimenting on a small plot can be motivated in different ways. For example, credit or cash constraints, which have been shown to be important in recent experimental studies on adoption (Karlan, et al., 2014; Duflo, Kremer, and Robinson, 2011) may force farmers to start small. More generally, low profitability and high uncertainty could also constrain the scale of experimentation. 16 Our model is related to those in Foster and Rosenzweig (1995) and Conley and Udry (2010) where farmers learn about the optimal level of fertilizers to be applied, which in our set-up corresponds to learning about the 𝑔𝑔() function. We consider learning about the quality of fertilizer rather than the optimal amount to apply. Indeed, to hone in on the dimension of learning that is relevant to our data we assume that farmers know the optimal quantities and how these (on average) translate into yields, 𝑔𝑔(𝜃𝜃), but they do not observe the quality of the technology. In the case of learning about the dilution of a single nutrient fertilizers we could in principle rewrite the model along the lines of Foster and Rosenzweig (1995) and Conley and Udry (2010) and let farmers experiment with identifying the right amount of fertilizer to apply to compensate for the unknown dilution level in the market.
17
(5) 𝜋𝜋(𝜃𝜃|𝜔𝜔1, … ,𝜔𝜔𝑎𝑎) =∏ 𝑓𝑓(𝜔𝜔𝑚𝑚|𝜃𝜃)𝑚𝑚 𝜋𝜋(𝜃𝜃)
∫ ∏ 𝑓𝑓(𝜔𝜔𝑚𝑚|𝜃𝜃)𝑚𝑚 𝜋𝜋(𝜃𝜃)𝑌𝑌𝜃𝜃10
,
where 𝜋𝜋(𝜃𝜃) is the initial prior density.
To examine the speed and ease of learning about quality, we consider a farmer’s confidence
in determining whether the fertilizer she is experimenting with is profitable or not in the sense
that it corresponds to a dilution level below or above the cut-off 𝜃𝜃∗. The posterior odds ratio; i.e.,
the probability that fertilizer is profitable given the observed signal relative to the probability that
fertilizer is not profitable given the signal is
(6) 𝑃𝑃�𝜃𝜃� ≤ 𝜃𝜃∗| 𝜔𝜔�𝑃𝑃�𝜃𝜃� > 𝜃𝜃∗| 𝜔𝜔�
=∫ 𝜋𝜋(𝜃𝜃)𝑌𝑌𝜃𝜃 𝜃𝜃∗
0
∫ 𝜋𝜋(𝜃𝜃)𝑌𝑌𝜃𝜃1𝜃𝜃∗
×∫𝑓𝑓(𝜔𝜔|𝜃𝜃,𝜃𝜃 ≤ 𝜃𝜃∗)𝜋𝜋(𝜃𝜃|𝜃𝜃 ≤ 𝜃𝜃∗)𝑌𝑌𝜃𝜃 ∫𝑓𝑓(𝜔𝜔|𝜃𝜃,𝜃𝜃 > 𝜃𝜃∗)𝜋𝜋(𝜃𝜃|𝜃𝜃 > 𝜃𝜃∗)𝑌𝑌𝜃𝜃
,
which is just the prior odds ratio times the ratio of marginal likelihoods, or the Bayes factor (see
Greenberg, 2013).
We consider two variants of the learning environment. In the first version, we assume that
farmers experiment with constant fertilizer quality 𝜃𝜃�, drawn from the market density. In the
second version we instead let farmers draw a new quality level 𝜃𝜃�𝑎𝑎 from the market density in
each period.17
The posterior odds ratio provides us with an illustrative way to examine the learning
environment without having to specify the relationship between quality, expected utility, and
demand. With more structure, however, we can also estimate the hypothetical farmer’s
willingness to pay (𝑊𝑊𝑊𝑊𝑃𝑃) for fertilizers as a function of the dilution rate 𝜃𝜃. To do so, we compare
the expected utility of adopting fertilizer, where the expectation is taken over the farmer’s
posterior density of fertilizer dilution given the harvests she has observed during experimentation,
to the certain return (in utility terms) of farming using traditional methods.18 Specifically, let the
systematic relationship between yield and quality of inputs be given by equation (2). We assume
17 A smaller follow-up study was implemented during the first season of 2016 (see online appendix). In the follow-up study, we repeatedly sampled (once every month) and tested DAP – a multinutrient fertilizer – from nine stores in three regions. Defining dilution of a DAP fertilizer sample as the weighted average of the dilution of the two main nutrients (nitrogen and phosphorus), we find an average dilution rate of 26%. Decomposing the variance, the between-store standard deviation is about five times larger than the within-store standard deviation, suggesting that the model variant in which farmers experiment with constant fertilizer quality is a more appropriate one. 18 The assumption that yield from farming with traditional methods is certain is a simplifying one and could be relaxed without changing the qualitative findings. However, as farmers have typically farmed with traditional methods over a long period and on a larger scale, presumably the uncertainty is significantly smaller than when experimenting with modern inputs.
18
that in order to invest in modern inputs, the farmer can borrow at a rate 𝑟𝑟 (or that is her outside
return on the funds used for investment). We further assume that utility is separable in
consumption and leisure. Given the results in Section V, we assume that the additional labor for
fertilizer use is hired labor, denoted 𝑌𝑌ℎ. The willingness to pay for fertilizer of quality 𝜃𝜃,
𝑊𝑊𝑊𝑊𝑃𝑃(𝜃𝜃), is then implicitly defined by equation (7),
(7) ∫ 𝜋𝜋(𝜃𝜃|𝜔𝜔1, . .𝜔𝜔𝑎𝑎)𝑢𝑢 �𝑝𝑝𝑚𝑚𝑔𝑔(𝜃𝜃) − (1 + 𝑟𝑟)�𝑌𝑌ℎ + 𝑊𝑊𝑊𝑊𝑃𝑃(𝜃𝜃)�� 𝑌𝑌𝜃𝜃 −10 𝜓𝜓(𝑌𝑌𝑓𝑓) ≥ 𝑢𝑢�𝑝𝑝𝑚𝑚𝑔𝑔(0)� −
𝜓𝜓(𝑌𝑌𝑓𝑓),
where 𝑌𝑌𝑓𝑓 is the amount of family labor and 𝜓𝜓(𝑌𝑌𝑓𝑓) the value of leisure. Note here that, consistent
with the assumption on the relationship between yield and the quality of inputs (equation (2)), we
assume that yield when adopting at scale (here normalized to one hectare) is given by 𝑔𝑔(𝜃𝜃).
Thus, in order to focus on how uncertainty about quality influences willingness to pay, we
abstract from the uncertainty related to the realization of yields for a given dilution level when
going to scale. However, as a comparison, we also report estimates of the 𝑊𝑊𝑊𝑊𝑃𝑃 that incorporate
such additional uncertainty (see Section VII.C.).
VII.B. Calibrating the Model
To use the model to assess farmers’ confidence in inferring quality and their willingness to
pay we need to solve equations (6)-(7).19 In order to do so we need to specify the systematic
relationship between yield (𝑦𝑦) and quality of inputs (𝜃𝜃); i.e., equation (2). We also need to
estimate the variance of the unobserved noise term 𝜎𝜎𝜀𝜀2 in the signal equation (3), determine the
profitability threshold 𝜃𝜃∗, and make an assumption about the farmer’s prior belief about the
distribution of fertilizer on the market, Π(𝜃𝜃). Finally, to estimate the willingness to pay we
further need to specify the price of maize and the cost of adoption and parameterize farmers’
preferences.
Consistent with the findings reported in Table II and illustrated in Figure IV, we assume that
the yield function, 𝑦𝑦 = 𝑔𝑔(𝜃𝜃), can be approximated by a linear function. We then use the
experimental yield data to estimate the parameters of this function. Specifically, using data from
the research managed trials, we estimate (by OLS)
(8) 𝑦𝑦𝑗𝑗 = 𝛼𝛼 + 𝛽𝛽𝜃𝜃𝜃𝜃𝑗𝑗 + 𝑌𝑌𝑗𝑗 ,
19 The integrals in equation (6) are evaluated numerically using Gauss-Chebyshev quadrature.
19
where 𝑦𝑦 denotes total yield per hectare, 𝜃𝜃 = (46 − %𝑁𝑁)/46, and subscript 𝑗𝑗 refers to a plot. To
consider learning about fertilizer quality, we consider one type of seed (farmer seeds), so we drop
sub-script 𝑘𝑘. As inputs where randomly assigned across plots, 𝛽𝛽𝜃𝜃 captures the causal effect of
inputs on yields.
Letting 𝑎𝑎 and 𝑏𝑏𝜃𝜃 denote the estimated parameters in equation (8), our empirical counterpart
of equation (3) is then given by,
(9) 𝑦𝑦 = 𝑔𝑔(𝜃𝜃) = 𝑎𝑎 + 𝑏𝑏𝜃𝜃𝜃𝜃 .
We also use experimental yield data to estimate the variance of the unobserved noise term.
Specifically, we use the distribution of the residual from regression (8) as an estimate of the
distribution of the noise in the signal equation; i.e. we set 𝜎𝜎𝜀𝜀2 = 𝜎𝜎𝑓𝑓2, where 𝜎𝜎𝑓𝑓2 is the variance of
the residual in regression (8). Thus, in essence we assume that the density of yields for a given
quality, derived using data from a large set of plots where identical inputs have been employed,
provides a good proxy for the uncertainty about quality that farmers face when experimenting on
their own plots. We then decompose this variation into two components: the variation accounted
for by the inputs, 𝑔𝑔(𝜃𝜃), and the unexplained variation; i.e., the noise term in equation (3).
Two remarks about this approach are in order. First, we assume that the noise term in the
signal equation (3) is homoscedastic; i.e., not a function of the level of dilution. A White (1980)
test for heteroskedasticity also confirms that this assumption is consistent with the data.20 Second,
an advantage of using data from the agricultural trials is that the variation in yields cross plots,
and especially the estimated noise in the data, for a given, randomly assigned technology bundle,
are not driven by variation in various farmer-specific factors or inflated by measurement error
problems. Nevertheless, it is possible that our estimate of the distribution of the noise in the
signal equation, and thus the learning environment, may not capture the learning environment
faced by many smallholder farmers very well. Our estimate may understate the learning problem
if farmers do not manage their plots consistently. We would also underestimate the severity of the
learning problem if experimentation primarily takes place over time, and farmers cannot perfectly
filter out ex post differences in weather shocks, and if the signal to noise ratio is a function of that
these shocks.21 Our estimate may overstate the learning problem if, for example, farmers
20 The standard deviation of the residual in regression (8), 𝜎𝜎𝑓𝑓, is 0.77. The test statistic for the null hypothesis of homoskedasticity is 𝜒𝜒2 = 4.23, with p-value= 0.13. 21 In a rain-fed irrigation system as in Uganda, the timing and level of rains matter for yields. The severity of the learning problem, however, depends on the signal-to-noise ratio (in model specifically the ratio 𝑏𝑏𝜃𝜃/𝜎𝜎𝑓𝑓). This implies,
20
experiment on larger plots than in our agricultural trials and the idiosyncratic variations we pick
up in the agricultural trials are decreasing in plot size, which seems likely.
To get a sense of how well our cross-sectional estimate captures the variance in returns
among farmers both over time and space, we exploit data from the Uganda LSMS-ISA. The
Uganda National Panel Surveys contain four waves of household survey data from which plot
specific measures of yield can be derived for two seasons each in 2009, 2010, 2011, and 2013. As
reported in Section II, relatively few farmers use fertilizers and hybrid seeds, so we focus on the
sub-sample of farmers using traditional farming methods. We then estimate a simple farmer fixed
effects regression (see online appendix), controlling only for plot size, and estimate the standard
deviation (𝜎𝜎𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿) of the residual from the regression and the relative standard deviation (the
standard deviation of the residual divided by the mean of the dependent variable). The results are
reported in Table A.2. Average maize yields vary between 1.3-1.6 metric tons per hectare, and
the relative standard deviation varies between 0.26-0.55, over the four waves (year). Pooling data
for all four years gives an average maize yield of 1.4 metric tons per hectare and a relative
standard deviation of 0.70. Using experimental data from the subset of plots with traditional
inputs (no fertilizer and traditional seeds), we estimate an average maize yield of 1.8 and a
relative standard deviation of 0.29. Thus while the variance in yield returns is larger in the LSMS
data relative to the experimental data, and especially so in the pooled data spanning five years,
the difference is relative modest, suggesting that the learning environment we study here is fairly
representative of the learning environment facing Ugandan farmers more generally.
Finally, we assume a 25% rate of return for profitability, which is close to the official
interest rate, and use equation (1) to back out the implied profitability threshold 𝜃𝜃∗, which from
Table V is a dilution rate of 17%, equivalent to 38%N.
To estimate the 𝑊𝑊𝑊𝑊𝑃𝑃, we use the estimates of price and costs as discussed in Section V and
assume that farmers have preferences that are characterized by constant relative risk aversion.22
VII.C. Results
We now use the learning framework derived above to start rationalizing the equilibrium we
observe. To do so, we investigate, within the model, Bayesian farmers’ ability to infer quality,
for example, that if we assume that yield is a linear function 𝜑𝜑𝑦𝑦��𝑛𝑛𝑗𝑗, 𝑠𝑠𝑘𝑘� of the state of nature 𝜑𝜑, then variations in 𝜑𝜑, while affecting both 𝑏𝑏𝜃𝜃 and 𝜎𝜎𝑓𝑓, will not affect the ratio 𝑏𝑏𝜃𝜃/𝜎𝜎𝑓𝑓. 22 For the main results, we assume that the coefficient of risk aversion is 2. We have found the results to be broadly the same for intermediate levels of risk aversion.
21
and willingness to pay, conditional on the level of dilution, when the farmers initially only know
the possible range of fertilizer dilution in the market; i.e. 𝜃𝜃 � ∈ [0, 1]. The first experiment thus
provides information about the likely quality range that would emerge in the market if farmers
initially have little information. We focus on three questions: (i) Is the learning environment
such that high levels of dilution will be found out very quickly and farmers would therefore not
be willing to pay for such fertilizers – consistent with the absence of fully diluted fertilizers in our
sample? (ii) Would risk-averse Bayesian farmers be willing to buy samples with intermediate
dilution levels – consistent with the range of dilution levels available in the market – and, is the
share of farmers willing to buy fertilizer similar to what is observed in the household data? (iii)
Finally, is the range of quality supplied in the market consistent with seller profit maximization
given farmers’ ability to learn and willingness to buy fertilizer of a given quality?
We then turn attention to a more hypothetical question: do sellers selling authentic fertilizer
have pecuniary incentives to enter the market given the surveyed farmers’ beliefs about fertilizer
quality, both under the status quo and when additional constraints are lifted?
A. Why does the market for fertilizer look like it does? As a first step towards understanding
why we observe the distribution of fertilizer quality that we do, we derive a relationship between
the dilution level of fertilizer and a Bayesian farmer’s ability to learn about fertilizer profitability
from experimentation. To trace out this relationship, we consider all possible dilution levels, i.e.,
𝜃𝜃 � ∈ [0, 1], and let the farmer experiment 1 …𝑊𝑊 times for each dilution level. We assume that the
farmer knows the range of fertilizer dilution, but has no other information. Her prior is thus best
described by a uniform distribution over [0,1]. We evaluate her confidence in inferring quality
when she receives an unbiased private signal 𝜔𝜔𝑎𝑎; i.e., the randomly drawn noise term 𝜀𝜀𝑎𝑎 takes the
value 0, about fertilizer quality after each period of experimentation.
In Figure VIII, Panel A, we plot the Bayesian farmer’s log10 odds ratio in favor of fertilizer
being unprofitable, log10 �𝑃𝑃(𝜃𝜃�> 𝜃𝜃∗)𝑃𝑃(𝜃𝜃�≤ 𝜃𝜃∗)
�, for each possible dilution level after 1, 5 and 10 rounds of
experimentation.23 We also categorize the learning environment, conditional on 𝜃𝜃�, into three
regions based on how fast the Bayesian farmer learns over time. To that end, we calculate the
23 We present the log10 odds ratio because of its symmetry properties: A log10 odds ratio of 1 implies that the farmer thinks it is ten times more likely that fertilizer is not profitable (than that it is) and a log10 odds ratio of -1 implies that she thinks it ten times more likely that fertilizer is profitable (than that it is not).
22
marginal likelihood after 5 periods; i.e., we filter out the prior by taking the difference between
the log10 posterior and prior odds ratio. Following standard notation, we then label an absolute
change in the log10 odds ratio of 1 or greater as regions characterized by strong learning; an
absolute change in the log10 odds ratio smaller than 1 but greater than 0.5 as a region
characterized by moderate learning, and an absolute change in the log10 odds ratio smaller than
0.5 as characterized by weak learning.24
There are large variations in the speed of learning across the range of dilution rates. For high
levels of dilution (𝜃𝜃� ≥ 0.5), learning is fast. As a result, the farmer quickly concludes that
fertilizer is unprofitable, with strong evidence against profitability accumulating after one (three)
[five] periods if the rate of dilution is above 55% (42%) [37%].
For intermediate dilution rates, however, learning is either moderately fast (0.40 < 𝜃𝜃� <
0.50) or slow (0.18 < 𝜃𝜃� ≤ 0.40), which implies that it takes more than 10 rounds of
experimentation to amass strong evidence that fertilizer of average quality is unprofitable.25 As
quality increases and fertilizer becomes profitable, learning speeds up again, but this is not
sufficient to convince the farmer that fertilizer is profitable given the initial beliefs. In fact, it
takes three or more rounds of experimentation to accumulate any evidence in favor of
profitability for most fertilizers in the authentic to almost authentic region (a shortfall of %N of
less than 10%), and even after ten periods, the evidence remains weak and inconclusive for most
fertilizers in this range.26
To show that farmers’ ability to learn about quality plausibly constrains the amount of
dilution in the market, we combine the relationship between dilution and learning with the
distribution of quality in the fertilizer samples purchased by the covert shoppers. In particular, in
24 Jeffreys (1961) and Kass and Raftery (1995) suggest interpreting the strength of the evidence in favor of model 𝑀𝑀1 as “decisive” if the posterior log odds ratio ≥ 2 in favor of model 𝑀𝑀1 relative 𝑀𝑀2, and as “strong” if the posterior log10 odds ratio ≥ 1 in favor of the alternative. If the posterior log10 odds ratio ≤ 0.5 but greater than 0, Jeffreys (1961) and Kass and Raftery (1995) label the evidence in favor of model 𝑀𝑀1 as “weak” or “inconclusive”. If 0.5 < posterior log10 odds ratio < 1, they suggest interpreting the evidence as “positive” or “moderate”. 25 Learning after one period in our model is slower than after the one harvest intervention in Hanna et al. (2014). In Hanna et al (2014) farmers are presented with information on optimal seaweed pod size based on a larger number of experiments, equivalent to many more rounds or larger scale of fertilizer experimentation in our model, while in our model farmers learn from experiments one plot/period at the time. 26 If we do not restrict attention to unbiased signals, so each farmer receives a unique sequence of signals, farmers will initially draw different conclusions about the quality on the market for a given quality. Random signals will also result farmers switching from being relatively confident that quality is high to quality being low. This result, in turn, may help explain why smallholder farmers, as documented in several studies (e.g. Duflo, Kremer, and Robinson, 2006; Suri, 2011; Dercon and Christiaensen, 2011), switch into and out of hybrid seed and fertilizer use over time.
23
Figure VIII, Panel B we plot the distribution function of fertilizer quality in the market samples
and overlay this with the learning regions from Panel A. Consistent with the finding that farmers
are able to deduce that fertilizer is not profitable when the dilution of nutrients in fertilizer is
high, we observe few samples with very low nitrogen content: less than 5% of samples lie in the
range where learning is fast (𝜃𝜃� > 50%). Conversely, approximately 60% of the samples are
located in the range where learning is slow and uncertainty about profitability is large.
Since farmers have great difficulty in determining the profitability of most of the fertilizers
in the market sample, it is natural to ask to what extent this affects demand. To answer this
question, we now consider at each dilution rate, 𝜃𝜃 � ∈ [0, 1], 𝑁𝑁 = 1000 initially uninformed
farmers. The farmers experiment with fertilizer of quality 𝜃𝜃� for 𝑊𝑊 rounds and receive a signal
with random noise about the fertilizer’s quality after each period. From this, we calculate each
farmer’s posterior distribution, their net expected utility and willingness to pay (see equation 7)
for fertilizer of dilution rate 𝜃𝜃� after 𝑡𝑡 = 1, … ,𝑊𝑊.
In Figure IX, Panel A, we plot the average as well as the 95th percentile of the willingness to
pay, normalized by dividing by the cost of adoption at average market prices, across the 𝑁𝑁
farmers at each dilution rate after 5 rounds of experimentation. For fertilizers with dilution rates
above 50%, no farmer has a 𝑊𝑊𝑊𝑊𝑃𝑃 above average market prices; i.e., farmers’ ability to detect
high dilution implies that farmers would not be willing to buy them at current market prices.
Turning to the moderately diluted fertilizers (<40% dilution), we see that lack of confidence
about profitability also constrains willingness to pay in this range: the average normalized 𝑊𝑊𝑊𝑊𝑃𝑃
is below the (average) market price for almost the full range of quality after 5 periods and rises
just above 1 for fertilizers with dilution levels of 4% or below.
For fully authentic quality, where the 𝑊𝑊𝑊𝑊𝑃𝑃 would be 55% above average market price if
quality was certain, it takes five periods before the average willingness to pay rises above the
average market price.
That the average willingness to pay is below average market price for almost all dilution
levels does not imply zero demand however. Learning implies that farmers respond to both signal
and noise, so there will be farmers who end up with a 𝑊𝑊𝑊𝑊𝑃𝑃 equal or above the (average) market
price at early stages of experimentation, even though for the most part fertilizer quality is too low
to be profitable. In fact, the 95th percentile of the 𝑊𝑊𝑊𝑊𝑃𝑃 is above the (average) market price after 5
periods of experimentation for dilution levels up to the mean market level (Figure IX, Panel A).
24
Hence there is a group of farmers with willingness to pay above market price, which consists of
two types: those who experiment with fertilizer that is not profitable but who have observed
higher than average yields (given the level of dilution) in a small number of experiments, and
those who experiment with fertilizer that is profitable.
Over time, as farmers become more confident about the quality of the fertilizer they are
experimenting with, the spread of the willingness to pay is reduced while its average increases.
Together these effects imply that the share of farmers willing to buy at market price increases for
profitable fertilizers, while it is more stagnant for unprofitable but not too highly diluted
fertilizers (0.3 < 𝜃𝜃 < 0.4) (see Figure IX, Panel B).
Combining this information with the distribution of dilution in the fertilizers we sampled as
part of the covert shopper approach (see Figure I), we can infer the likely demand sellers would
face if prices are fixed. Assuming that farmers experiment with constant fertilizer quality 𝜃𝜃�
drawn randomly from the market distribution, we find that 12.5 percent of farmers end up with a
willingness to pay equal to or higher than the current market price after 5 rounds of
experimentation (see Table VII, Panel A). Of these, just over a third would buy from sellers
selling profitable fertilizer and just under two thirds would be overly optimistic and buy from
sellers with moderate dilution rates. If instead, farmers drew a new quality level 𝜃𝜃�𝑎𝑎 from the
market density in each period, the share of farmers with a willingness to pay at least average
market price is halved after five periods. This is the case because the additional uncertainty that
comes with the variation in 𝜃𝜃� complicates the inference problem even more.
As time passes, the share of farmers with a willingness to pay greater than the market price
increases, but the composition of demand remains fairly constant, at least over the medium run.
Of course, with Bayesian learning, the proportion of overly optimistic farmers willing to buy
unprofitable fertilizer would eventually shrink to zero. But this happens quite slowly, even after
20 periods of experimentation, when around one in five farmers are willing to buy at market
price, the share of those buying unprofitable fertilizer is still roughly 50%. Put another way, in
our model, a seller selling unprofitable but not too diluted fertilizers, can still expect to capture an
– albeit small – part of the market for a relatively long period of time.
Table VII, Panel B, reports the closest empirical counterpart, using data from the household
survey, to the estimates in Panel A. Urea use varied between 10.2% and 12.6% over the last two
seasons – numbers that are similar to the 13% (17%) of farmers with a 𝑊𝑊𝑊𝑊𝑃𝑃 above the (average)
25
market price in the model after 5 (10) periods. Moreover, conditional on using urea in the first of
the two seasons for which we have data, 59.5% continue to use it the following period, which
again is broadly consistent with the model’s prediction that about half of the farmers with a 𝑊𝑊𝑊𝑊𝑃𝑃
above the (average) market price buy from sellers selling profitable fertilizer, assuming that
farmers that manage to buy fertilizers of sufficiently high quality would continue to do so.
Finally, we ask whether the range of quality observed in the market could be consistent with
sellers who maximize profits taking farmer’s willingness to pay for fertilizer as given. If we
assume that sellers are local monopolists and compete on quality; i.e., the price is fixed or taken
as given, then the share of farmers with willingness to pay above the (average) market price in
Figure IX, Panel B could be interpreted as the seller’s demand as a function of dilution. If in
addition, the cost of supplying quality is increasing and convex, it is straightforward to show that
the profit-maximizing dilution level is increasing in the slope of the demand curve.27 That is, the
steeper the demand curve, the lower dilution. As illustrated in Panel B, as farmers become more
confident in drawing (correct) conclusions about the quality in the market, the “demand” curve
becomes steeper. Thus, within the context of this extended model, improved precision in learning
about quality maps into higher quality. That is, a potential explanation for part of the variation in
quality we observe across sellers is that farmers’ ability to infer quality differs across locations.
Taken together the results show that high dilution rates will be found out quickly. As a
result, farmers would not buy fertilizers of too low quality and the incentives to sell these highly
diluted fertilizers should be weak. On the other side of the spectrum, it is difficult, and takes time,
for farmers to accumulate evidence that authentic or close to authentic fertilizers are sold, when
that is in fact the case. This implies that it will take a long time for sellers to build up a reputation
as a high quality retailer, and price their products accordingly. At the same time, as profit margins
are presumably in some way related to the rate of dilution of fertilizer, sellers likely have strong
short run incentives not to sell high quality. In fact, given the unregulated and unmonitored
market structure, and the difficultly farmers face in learning about profitable fertilizers, the
question may not be why we observe widespread dilution of fertilizers on the market, but why
any seller would supply profitable fertilizers without a mark-up, which we do observe. The
27 Denote demand as a function of dilution by 𝑌𝑌(𝜃𝜃) and cost by 𝑐𝑐(𝜃𝜃). Profit maximization implies that 𝑝𝑝𝑌𝑌𝜃𝜃(𝜃𝜃) =𝑐𝑐𝜃𝜃(𝜃𝜃), with a maximum implying 𝑝𝑝𝑌𝑌𝜃𝜃𝜃𝜃 < 𝑐𝑐𝜃𝜃𝜃𝜃 . Differentiating the first-order condition and rearranging gives 𝜕𝜕𝜃𝜃
𝜕𝜕𝑑𝑑𝜃𝜃(𝜃𝜃)= −1
𝑝𝑝𝑑𝑑𝜃𝜃𝜃𝜃− 𝑒𝑒𝜃𝜃𝜃𝜃 , which is greater than zero from the second-order condition.
26
answer is likely that at least some sellers have important intrinsic and nonpecuniary motivations
not to sell inputs of too low quality. Finally, and consistent with the evidence from the farmer
survey, we have shown that the market does not collapse. Some farmers do buy. In the model
they do so because they either have managed to purchase profitable fertilizers or because they are
overly optimistic after receiving (a series of) positive yield shocks.
B. A market for high quality? Having focused on explaining the market as is, we now move
to a more hypothetical question: what would happen if a seller committed to high quality entered
the market and started selling fertilizer to farmers, and in particular, to the farmers surveyed in
our study. Assuming that farmers are Bayesian, and given the farmers’ (initial) distribution about
quality, we investigate whether a seller committed to high quality would be able to build up a
reputation for selling profitable fertilizer and price its product accordingly, both under the status
quo and when additional constraints that might improve the learning environment are lifted. This
is an interesting counterfactual policy question since a potential intervention to overcome the
lemons problem in the market for fertilizer could be the entry of an NGO or a private firm who
sells the highest possible quality, not necessarily at a subsidized price and without a strong
reputation to begin with. Thus, we are interested in understanding how beliefs, willingness to pay
and adoption would evolve over time given existing (prior) beliefs among farmers in our data.
We determine the rate of learning about authentic quality and what farmers are willing to
pay for such quality by letting each of the 𝑁𝑁 farmers in our survey experiment for 𝑊𝑊 periods with
authentic fertilizer.28 For each farmer, we derive the prior density of dilution rates from her
reported distribution of fertilizer quality in the nearest shop. Following each round of
experimentation, the farmer receives an unbiased signal with standard deviation 𝜎𝜎𝜀𝜀 about
fertilizer quality, where we use either the estimate from the experimental data as before or a fifty
percent higher level to account for additional uncertainty at the farmer level. The farmer updates
her posterior density according to Bayes Law and we can then use this density to calculate the
distribution of confidence and the willingness to pay for authentic fertilizer in the sample of
farmers we surveyed.
Consistent with the previous analysis, being confident that fertilizer is profitable takes time
even for the – slightly more optimistic – farmers in our survey. After five rounds of
28 To account for some quality shortfalls even from a seller committed to high quality, we assume that fertilizer quality is uniformly distributed on the “almost authentic” interval 𝜃𝜃 ∈ [0,0.1].
27
experimentation, only 16 percent of farmers have strong evidence in favor of profitability. This
number is even lower (less than one in ten) if the noise experienced by farmers is larger than the
benchmark estimate (Figure A.4). Similarly, few farmers are willing to buy, at least initially: only
one in five farmers has a willingness to pay above market price after experimenting once and this
drops to less than one in ten if learning is even noisier. While this number rises to 70% and 50%
respectively after five periods of experimentation, the average willingness to pay only just
exceeds market price at this stage and the average margin for those with a willingness to pay
above market price is roughly half of that which would obtain if quality was known with
certainty.29 Hence a seller committed to high quality could potentially establish themselves, but
only if they are in it for the long haul. Moreover, such a seller could either capture a large share
of the market or raise prices, but would struggle to do both.
Our analysis so far is based on a set of parameters estimated directly from the data.
Importantly, several of these parameters, in turn, are determined by factors we do not study here
but that relate directly or indirectly to several constraints to adoption that have been highlighted
in the recent literature. For example, lack of information about optimal agricultural practice and
the use of the technologies has a direct effect on profits and thus the farmers’ willingness to
adopt.30 It may also affect the variability in returns to adoption (or to farming in general) and
thereby farmers’ ability to infer quality.
Learning about quality would in principle also be enhanced by combining more information
sources; i.e., through social rather than individual learning.31 Observing technology choices and
yield from other farmers will increase the number of signals a farmer would receive at each point
in time and thereby speed up the process of learning about quality. However, as the signal to
noise ratio when learning from others is affected by the heterogeneity in plot characteristics and
especially farmer characteristics (Munshi, 2004), it may also complicate the inference problem.32
29 Adding uncertainty to the realization of yields for a given dilution level when going to scale (see Section VII.A) lowers the willingness to pay even further (see Figure A.3), although the fall in the 𝑊𝑊𝑊𝑊𝑃𝑃 is relatively small. 30 Duflo, Kremer, and Robinson (2006) show that intensive extension work significantly increased the use of fertilizers, although the quantitative effects were quite small. 31 On social learning about expected yield, see e.g., Besley and Case (1994) and Munshi (2004). On social learning about optimal input application, see e.g., Foster and Rosenzweig (1995), Conley and Udry (2010), and Duflo et al (2006). The empirical evidence is somewhat mixed, with Foster and Rosenzweig (1995) and Conley and Udry (2010) showing evidence in favor of social learning while Duflo et al. (2006) showing that information from neighbors plays a very limited role in decisions about fertilizer use. 32 The less a farmer is able to observe actions and characteristics of her peers, the more difficult it will be for her to accurately assess the available information, and the more likely that the farmer makes mistakes.
28
Both fertilizers and hybrid seeds are divisible and standard theory does therefore not predict
that credit constraints can explain why farmers do not use these technologies at all.33,34 Liquidity
and risk constraints, however, do not only have a potential direct effect on farmers’ willingness to
adopt but could also affect farmers’ ability to learn about quality by forcing farmers to
experiment at small scale – as we assume in our learning model.35 Having access to insurance
markets and not facing any liquidity constraints should allow farmers to experiment on a larger
plot. This in turn will likely attenuate some of the measurement error in the signal equation (3)
and thus increase the signal to noise ratio.
Assuming the relaxation of credit, liquidity and information constraints increases the signal
to noise ratio, we can zero in on one potential mechanism through which the relaxation of these
constraints may impact the market for high quality. Specifically, we repeat the analysis of letting
the farmers in our survey experiment for 𝑊𝑊 periods with authentic fertilizer, but reduce the noise
on the quality signal.
If farmers could experiment in a less noisy environment, confidence about quality and
therefore the seller’s ability to price her products appropriately would increase faster (Figure
A.4): with noise equivalent to fifty percent of the original standard deviation, half the farmers
would have strong evidence that fertilizer is profitable after five periods of experimentation and
90% would have a willingness to pay above 1, with the average margin around two thirds of that
obtained under certainty. Of course, this margin in turn is constrained by the relatively high
required rate of return on fertilizer. Inasmuch as access to insurance and credit markets would
reduce the required rate of return, the potential profits of the seller and hence the incentives to
sell authentic fertilizer would increase even further.
To sum up, the results with a higher signal to noise ratio suggest that by addressing
constraints we know are limiting farmers’ willingness to adopt modern technologies, one can,
33 This no longer holds if there are fixed costs to adoption, for instance fixed costs in buying the inputs. Such fixed costs would have to be implausibly large, however, to justify the lack of investment in fertilizers and/or hybrid seeds in the standard model (see discussion in Duflo et al, 2011). 34 Experimental evidence on technology adoption in agriculture suggest that credit constraints are not a binding constraint for most farmers. Financial barriers, however, go beyond a lack of credit access. Karlan et al. (2012) find substantial demand for index insurance and a strong effect of insurance on agricultural investments. Duflo et al., (2011) show that providing farmers with a commitment savings technology substantially increased fertilizer use. 35 Farmers may be forced to experiment with modern inputs on a small plot due to credit and cash constraints. They may also choose to experiment on a small scale for other reasons. The 𝑊𝑊𝑊𝑊𝑃𝑃 based on the priors for most farmers in the sample is below 1. Farmers might thus consider buying for a small part of the field to reduce their uncertainty about profits; i.e. low profitability and high uncertainty may also constrain the scale of experimentation.
29
through affecting the speed and strength of learning and thereby sellers’ incentive to supply high
quality, also potentially mitigate the market of lemon problem in agricultural input markets.
VIII. DISCUSSION
We find that the quality of fertilizers and hybrid seeds sold in local markets in two of the
main maize-growing regions of Uganda is low on average. Moreover, under reasonable
assumptions on costs, the return to adoption of such substandard inputs is low. The rate of return
of using authentic fertilizer and hybrid seed is large, however. Together, our results suggest that
one reason smallholder farmers do not adopt fertilizer and hybrid seeds is that the technologies,
available in local markets are simply not very profitable.
We further provide evidence of the learning environment facing smallholder farmers,
showing that farmers can likely infer that inputs are of poor quality if the quality of the inputs is
sufficiently low, but find it hard to detect whether the large majority of substandard fertilizers
observed in the market place are profitable or not. Moreover, we argue that the sellers’ pecuniary
incentives to build up a high quality reputation are likely weak, as farmers cannot distinguish
authentic from slightly lower quality and farmers’ willingness to pay falls relatively little as
quality falls, at least starting at low levels of dilutions. This finding may help explain why we do
not observe sellers selling high quality at a premium price.
Our findings imply interesting avenues for future research. Low quality could be due to a
multitude of factors, including adulteration, poor storage and inappropriate handling procedures.
Moreover, quality deterioration could manifest at different points in the supply chain. Anecdotal
evidence and news reports suggest that adulteration, by bulking out fertilizer or dyeing simple
grain to look like hybrid seeds, is common, but more research is needed to determine if this is
indeed the case. While the exact reasons may be irrelevant for a farmer’s decision to adopt,
understanding the determinants of quality is important for policy.36
More generally, our findings highlight the need to identify ways to substantially increase the
quality of basic agricultural technologies available to smallholder farmers. An obvious follow-up
question to our work is how the rate of technology adoption and productivity would change if
36 Agricultural technologies such as fertilizer and hybrid seeds form part of a wider set of products or inputs where quality is not directly observable at the time of purchase, and only partially observable when used. Anecdotal evidence and news reports suggest that product quality in markets for experience goods more broadly is notoriously low in developing countries. Recent work on poor quality medicine in developing countries is a case in point (see e.g. Bennett and Yin, 2014; and Bjorkman, et al. 2012).
30
smallholder farmers could access high quality inputs and whether adoption rates could be further
boosted by addressing other binding adoption constraints as our analysis suggests.
The low technology adoption rates in Sub-Saharan Africa are likely caused by several
interrelated factors, as the recent experimental literature has shown. Importantly, even if farmers’
decisions whether to use fertilizers and hybrid seeds are not primarily constrained by the low
quality of the technologies in the market place, the low quality has a first-order impact on the
income and welfare of smallholder farmers who adopt. For adopters we estimate that the loss in
revenues, per hectare of land, due to substandard quality, is US$250 on average; i.e. for average
market quality, per season. As a reference, the revenue from traditional farming, the main source
of income for poor small-holder farmers, per hectare of land and season, is estimated to be just
over US$320.
SUPPLEMENTARY MATERIAL
An Online Appendix for this article can be found at QJE online (qje.oxfordjournals.org).
INSTITUTE FOR INTERNATIONAL ECONOMIC STUDIES, STOCKHOLM UNIVERSITY,
CENTER FOR ECONOMIC AND POLICY RESEARCH
NATIONAL AGRICULTURAL RESEARCH LABORATORIES, KAMPALA
INSTITUTE FOR INTERNATIONAL ECONOMIC STUDIES, STOCKHOLM UNIVERSITY,
CENTER FOR ECONOMIC AND POLICY RESEARCH
UNIVERSITY OF ZURICH, NATIONAL BUREAU FOR ECONOMIC RESEARCH
31
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34
TABLE I
PERCENT NITROGEN (%N) IN RETAIL FERTILIZERS (UREA)
Mean Standard deviation Minimum Maximum Observations
%N 31.8 5.6 8.1 44.3 369
Notes. Summary statistics on the nitrogen content of the 369 fertilizer samples purchased in the covert shopper exercise and analyzed in the laboratory.
35
TABLE II
YIELD RETURN (METRIC TONS PER HECTARE) TO INCREASING QUALITY OF FERTILIZERS
Specification (1) (2) (3) (4)
Farmer Experimental sites Farmer survey
%N 0.049*** 0.057*** 0.065***
(0.004) (0.004) (0.005)
Expected %N 0.060**
(0.024)
Constant 1.973*** 2.268*** 2.600*** 0.82
(0.095) (0.087) (0.126) (0.56)
Observations 150 150 150 292 R-squared 0.52 0.65 0.52 0.02 Seeds Farmer Hybrid market Hybrid
authentic Farmer
Unit of Analysis Plots Plots Plots Farmers
Notes. Values shown are coefficients from ordinary least squares regression. Each column represents a different regression. The dependent variable in columns (1)-(3) is maize yield (metric tons per hectare) on experimental plots. The independent variable is content of nitrogen (percent Nitrogen; %N) in the fertilizer applied to the experimental plot. The dependent variable in column (4) is expected maize yield (metric tons per hectare) based on farmer survey data and the independent variable is expected content of nitrogen (percent Nitrogen; %N) in the nearest retail shop. The p-value on the test of the null hypothesis that the coefficients in specifications (1) and (2) [(1) and (3)] {(2) and (3)} are equal is 0.00 [0.02] {0.02}. Robust standard errors in parentheses. *** 1% , ** 5% , * 10% significance.
36
TABLE III
ESTIMATES OF QUALITY OF RETAIL HYBRID SEED BASED ON ITS YIELD
(1) (2)
Retail hybrid
seeds Mix of authentic and
farmer seeds
α 0.52
(0.11)
Mean 3.563 3.566 Variance 1.172 1.264 Skewness -0.058 -0.069 Kurtosis 2.437 2.123 Criterion value 1.63
Notes. The unit of observation is a stratum, which contains the plots that are on the same site and block and have fertilizer with the same level of nitrogen applied to them. Column (1) contains the first four moments from the observed distribution of yields (metric tons per hectare) planting retail hybrid seed averaged at the stratum level. Column (2) presents the estimate of α that minimizes the squared weighted distance between the first four moments of this distribution and a simulated distribution of yields constructed by combining the maize yield from plots growing farmer seed and the maize yield from plots growing authentic hybrid seed in each stratum using the ratio 𝛼𝛼: 1 − 𝛼𝛼. The first four moments of this simulated distribution, as well as the value of the criterion at the estimated 𝛼𝛼, are also reported. Standard errors in parentheses are bootstrapped drawing 1,000 samples from the yield distribution.
37
TABLE IV
COMPLEMENTARY LABOR INPUTS
Specification
(1) Family
labor (days)
(2) Family
labor (days)
(3) Expenses on hired labor
(4) Expenses on hired labor
Using fertilizer 32.4 (24.5)
10.2 (17.1)
197,566*
(101,310) 127,875*
(67,091) Using improved seeds 1.52
(12.5) -3.58 (11.6)
119,267***
(38,660) 103,220**
(40,231) Using fertilizer & improved seeds 30.7
(28.7) 96,708
(136,274) Constant 105.7***
(9.59) 107.7***
(8.7) 70,288**
(32,922) 76,739*
(28,409)
p-value: F-test (fertilizer, seeds) 0.37 0.69 0.02 0.04 Observations 312 312 310 310
Notes. Labor inputs conditional on technology adoption. Unit of observation is a household. OLS estimates from a linear regression with location (trading center) fixed effects. Improved seeds are either open-pollinated varieties (OPV) or hybrid seeds. Family labor is adult labor days per season, with working day normalized to eight hours. Expenses on hired labor per hectare in Ugandan shillings per season, UGX (exchange rate was approximately UGX 3,200=$1). F-test is the test of the null hypothesis (𝛽𝛽𝐹𝐹𝑓𝑓𝑓𝑓𝑎𝑎𝑚𝑚𝐹𝐹𝑚𝑚𝐹𝐹𝑓𝑓𝑓𝑓 = 0 and 𝛽𝛽𝐿𝐿𝑓𝑓𝑓𝑓𝑑𝑑 = 0). Standard errors clustered by location (trading center) are in parentheses. *** 1% , ** 5% , * 10% significance.
38
TABLE V
ECONOMIC RETURNS TO FERTILIZER AND HYBRID SEEDS ADOPTION
Source:
(1) Technologies
available in the market
(2) Authentic
technologies
Panel A: Adoption of UREA fertilizers and hybrid seeds
Mean rate of return 6.5% 83.6%
Median rate of return 10.8% 83.1%
Fertilizer samples yielding positive net-return 65.6% 100.0%
Fertilizer samples yielding rate of return > 25% 8.9% 100.0%
Fertilizer samples yielding rate of return > 50% 0.0% 100.0%
Panel B: 25% lower complementary expenses
Mean rate of return 15.8% 99.6%
Median rate of return 20.5% 99.0%
Fertilizer samples yielding positive net-return 76.7% 100.0%
Fertilizer samples yielding rate of return > 25% 37.1% 100.0%
Fertilizer samples yielding rate of return > 50% 1.1% 100.0%
Panel C: 50% lower complementary expenses
Mean rate of return 26.9% 118.7%
Median rate of return 31.9% 117.9%
Fertilizer samples yielding positive net-return 89.2% 100.0%
Fertilizer samples yielding rate of return > 25% 62.3% 100.0%
Fertilizer samples yielding rate of return > 50% 7.9% 100.0%
Notes. Average and median rate of return, and threshold values, for adopting fertilizer and hybrid seed on one hectare of land. The unit of observation is a fertilizer sample. Column (1) presents the rate of return of technologies available in the market and column (2) presents the rate of return if technologies were authentic. Panel A, baseline scenario (see text for details). Panel B reports returns assuming 25% lower complementary labor expenses and Panel C reports returns assuming 50% lower complementary labor expenses compared to the baseline scenario reported in Panel A.
39
TABLE VI
FARMER BELIEFS: PERCENT NITROGEN (%N) IN NEAREST SHOP
Mean Std Min Max Obs
%N 28.4 8.0 4.6 46 295
Notes. The values provide summary statistics of the expected nitrogen content in the nearest retail shop from the farmer survey. See text and online appendix (A2) for details.
40
TABLE VII
WILLINGNESS TO PAY (WTP) AND ADOPTION RATES
Panel A: Model estimates
𝑊𝑊𝑊𝑊𝑃𝑃 > 1 (𝑊𝑊𝑊𝑊𝑃𝑃|𝜃𝜃� ≤ 𝜃𝜃∗) > 1
Periods of experimentation 3 5 15 3 5 15
Share of farmers (constant quality draws)
7.7% 12.5% 17.9% 2.7% 4.5% 7.8%
Share of farmers (time variant quality draws)
6.3% 6.4% 5% - - -
Panel B: Household survey data Used urea in last seasons Conditional on urea
use in season 1, used urea in season 2 Season 1 Season 2
Share of farmers 12.6% 10.2% 59.5%
Number of farmers 294 295 294
Notes. Panel A reports estimates from the Bayesian model (see text for details). The first three columns (𝑊𝑊𝑊𝑊𝑃𝑃 > 1) depict the share of farmers (after 3, 5 and 15 periods) with a normalized willingness to pay above the (average) market price and the three last columns (𝑊𝑊𝑊𝑊𝑃𝑃|𝜃𝜃� ≤ 𝜃𝜃∗) > 1 depict the share of farmers (after 3, 5 and 15 periods) with a normalized willingness to pay above the (average) market price conditional on drawing a profitable fertilizer sample (𝜃𝜃� ≤ 𝜃𝜃∗). The first row reports the results when farmers experiment with constant fertilizer quality 𝜃𝜃� drawn randomly from the market distribution. The second row reports the results when farmers draw a new quality level 𝜃𝜃�𝑎𝑎 from the market density in each period. Panel B reports summary statistics from the household survey data. The first two columns report the share of farmers, by season (first and second season of 2013), reporting to have used urea on at least one plot. The last column reports the share of farmers that continued to use urea on at least one plot in season 2, conditional on using urea in season 1.
41
The bars present the percentage of the 369 fertilizer samples with nitrogen content equal to the values shown on the X-axis. The dashed vertical line indicates the amount of nitrogen in authentic fertilizer. Data from the covert shopper survey, with percent Nitrogen (%N) tested in the lab.
FIGURE I
The distribution of nitrogen content in fertilizer
0.0
2.0
4.0
6.0
8.1
Dens
ity
10 20 30 40 50Percent Nitrogen (%N)
42
The dots show the combination of nitrogen content and price per kilogram of urea for each of the 369 fertilizer samples. The solid line is based on a local polynomial regression fitted to the data and the grey shaded area represents the 95% confidence interval. Data from the covert shopper survey with percent Nitrogen (%N) tested in the lab.
FIGURE II
The relationship between price and quality of fertilizer
2000
2500
3000
3500
4000
Price
(UG
X) p
er k
ilogr
am o
f URE
A
10 20 30 40 50Nitrogen content of fertilizer (%N)
43
The bars present maize yield in metric tons per hectare growing farmer seed (leftmost panel), retail hybrid seed (middle panel) and authentic hybrid seed (rightmost panel) after applying fertilizer with percent Nitrogen (%N) given by 0%N, 11%N, 23%N, 34%N or 46%N. The error bars represent the 95-percent confidence interval. The unit of observation is an experimental plot. Data from the experimental plots.
FIGURE III
The yield return to nitrogen content in fertilizer
44
Nonparametric Fan regression of yield (metric tons per hectare) on percent Nitrogen (%N) in fertilizers with authentic seeds. The unit of observation is an experimental plot. Data from the experimental plots.
FIGURE IV
The yield return to increasing quality of fertilizers
02
46
8Yi
eld
0 10 20 30 40 50Percent Nitrogen (%N)
45
The bars present the percentage of farmers’ beliefs about nitrogen content (percent Nitrogen; %N). Data from the household survey. 295 farmers.
FIGURE V
Farmer beliefs: Percent Nitrogen (%N) in nearest shop
0.0
1.0
2.0
3.0
4.0
5De
nsity
0 10 20 30 40 50Percent Nitrogen (%N)
46
The solid line represents the cumulative distribution of expected yields in metric tons per hectare when using authentic fertilizer. The dotted line represents the cumulative distribution of expected yields when using retail fertilizer. The dashed line represents the cumulative distribution of expected yields when not using fertilizer. Data from the household survey.
FIGURE VI
Farmer expectations: Cumulative distribution of maize yield
47
The density, for each quality combination, is based on 30 randomly assigned plots observations from the research managed trials. The solid line depicts the density of yields (metric tons per hectare) when using authentic fertilizer (%N=46) and farmer seeds. The dashed line depicts the density of yields when using technologies with close to mean market quality (%N=23) and farmer seeds. The dashed-dotted line depicts the density of yields when using the technologies with the lowest quality (%N=0) and farmer seeds. Data from the experimental plots.
FIGURE VII
Densities of yield for different input qualities
48
Panel A: Evidence in favor of fertilizer being profitable or not
Panel B: Learning about fertilizer quality and distribution of market fertilizers Panel A: Log10 odds ratios in favor of fertilizers being profitable relative being unprofitable after 1 (solid line), 5 (dashed line), 10 (dashed-dotted line) rounds of experimentation. Panel B: Distribution function of fertilizer quality in the market (solid line). Strong learning if the absolute change in the log10 odds ratio (marginal likelihood) is greater or equal to 1; moderate learning if the absolute change in the log10 odds ratio is smaller than 1 but greater than or equal to 0.5; and weak learning if the absolute change in the log10 odds ratio is smaller than 0.5.
FIGURE VIII
Learning about fertilizer quality: Evidence in favor of fertilizer being profitable or not
Moderate learning
Moderate learning
Weak learning
Dilution of fertilizer
Moderate learning
Weak learning
Moderate learning
Strong learning
after 1 harvest after 5 harvests after 10 harvests
Log1
0 O
dds r
atio
in fa
vor o
f un
prof
itabl
e fe
rtiliz
er
Dilution of fertilizer
Dis
tribu
tion
of m
arke
t fer
tiliz
er
Strong learning
49
Panel A: Willingness to pay (𝑊𝑊𝑊𝑊𝑃𝑃) after 5 periods
Panel B: Share of farmers with a willingness to pay above the average market price
Panel A: Average (solid line) and the 95th percentile (dashed-dotted line) of the normalized willingness to pay conditional on the level of dilution of fertilizers after 5 periods of experimentation. Panel B: Share of farmers with a willingness to pay above the (average) market price (𝑊𝑊𝑊𝑊𝑃𝑃 > 1) after 3 (sold line) and 5 (dashed line) periods.
FIGURE IX
Willingness to pay (𝑊𝑊𝑊𝑊𝑃𝑃)
Shar
e of
farm
ers
after 3 periods after 5 periods
Dilution of fertilizer
Will
ingn
ess t
o pa
y
Mean 95th percentile
Supplemental Online Appendix for:
“LEMON TECHNOLOGIES AND ADOPTION: MEASUREMENT, THEORY AND EVIDENCE FROM AGRICULTURAL MARKETS IN UGANDA”
Tessa Bold, Kayuki C. Kaizzi, Jakob Svensson, David Yanagizawa-Drott
December 2016
This PDF file includes:
Supplementary Text (Sections A.1-A.8)
Tables A.1 to A.4
Figures A.1 to A.4
Content
A. Measurement and data
A.1 Measuring the quality of fertilizers and seeds
A.2 Crop management and data collection protocol
A.3 Measuring the quality of retail hybrid seeds
A.4 Household survey
A.5 LSMS data and estimation of the residual and the CV
A.6 2016 Follow-up study
A.7 Additional calculations
A.8 Additional references
B. Additional tables
Table A.1 Percent of households using fertilizer and improved seed varieties
Table A.2 Estimates of the distribution of the noise in the signal equation
Table A.3 Rate of dilution (%) of DAP retail fertilizers
Table A.4 Descriptive statistics for the household survey based variables
C. Additional figures
Figure A.1 The yield distribution of retail hybrid seed and the simulated seed
Figure A.2 Rate of returns to technology adoption as a function of average yield
Figure A.3 Willingness to pay: Adding uncertainty to the realization of yields when
adopting at scale
Figure A.4 Market for high quality
A.1. Measuring the quality of fertilizers and seeds
The purchases of urea were done in connection with the first planting seasons of 2013 and
2014. We conducted the sampling of retail shops in two steps: first, in each year we randomly
selected districts from two of the main maize-growing regions (eastern and western regions),
and second, in each district we enumerated all trading centers and randomly selected a total
of 20 trading centers. We then sampled up to three retail shops in each trading center. In total,
96 agro-input retailers were sampled, 50 in 2013 and the remainder in 2014. In addition, 33
retailers operating in the main agro-inputs market in Kampala ("Container village") were
randomly selected and visited in 2014, yielding a total sample of 129 retail stores.
We sent covert shoppers to purchase the samples we tested. We trained a set of
enumerators with knowledge of the local area and language, and gave them a prepared script
for how to buy the inputs. These covert shoppers were impersonating poor farmers from the
area, with clothing and accessories chosen accordingly, with the objective of mimicking the
purchase of a farmer wanting to begin using fertilizer. We deemed the design appropriate for
this purpose, as agro-input retailers in the trading centers, and in Container village, serve
large potential customer bases.
Between 1–6 bags of 1–2 kilograms each were purchased from each retailer outside of
the main agro-inputs market in Kampala. For the random subset of retailers where multiple
purchases were done, two covert shoppers were used, buying on up to three different days,
with at least two weeks between purchases. In the main agro-inputs market in Kampala, it is
common to buy fertilizer in larger quantities. For that reason, two 50-kilogram bags were
purchased by two different buyers from each of the retailers sampled in Container village. In
total, 369 samples were purchased.
After the purchase was completed, and once out of sight of the shop, the surveyor
recorded the price of the sample. The samples were then transferred to Kampala. Each sample
was tested three times for the content of nitrogen (N) using the Kjeldahl method (Anderson
and Ingram, 1993) at the Kawanda Agricultural Research Institute laboratory. We use the
mean of these tests to determine the quality of a sample. Authentic urea should contain 46%
nitrogen.
The purchase of retail hybrid seed followed a similar design. Close to the planting
season in 2014, we identified the 15 closest trading centers surrounding the five research
stations. We enumerated stores in each trading center and randomly selected 30. According to
the script, the covert shoppers bought 2–6 kilograms of the same branded seed type as the
authentic hybrid seed. If the retailer did not carry that particular hybrid seed, the shopper did
not buy, and the team selected a replacement shop.
For farmer seed, we enumerated the villages in a 20-kilometer radius around the
research stations and randomly picked 6–9 villages per site. In each village covert shoppers
(farmers) bought approximately 3 kilograms of farmer seeds from two farmers.
A.2. Crop management and data collection protocol
The crop management and data collection protocol followed the methodology outlined in
Kaizzi et al. (2012). All five sites were managed by the research team and the staff assigned
to implement the trial protocol were blinded to treatment status of the plots. At each site the
field was ploughed and harrowed. 10-15 soil samples were collected from each research field.
The results of the soil analysis indicate that on average, the fields had low levels of soil
organic matter (SOM), available P (Phosphorus) and total N (Nitrogen) and low to average
levels of available K (Potassium). Specifically, across the five sites, the levels of soil organic
matter (SOM) – the major source of nutrients in the soils – were below or close to the
commonly used critical level (Loveland and Webb, 2003).
In each plot, 7 rows of seed were planted, with a spacing of 75 cm between rows. In
each row two maize seeds were planted per hill with a spacing of 30 cm between hills, for a
total of 105 hills per plot. Fertilizer was applied at 108 kilograms per hectare (which
corresponds to the official recommendation of 50kg N/ha) in two splits: 54 kg/ha at planting
by broadcasting and immediately incorporating into the soil and later at tasselling top dress
with the remaining 54kg/ha. At 2–3 weeks after emergence, the plants were counted, weeded,
and thinned to one plant per hill. The harvest was done excluding the outer perimeter of the
plot and the grains were oven dried to correct for moisture.
A.3. Measuring the quality of retail hybrid seeds
To infer the quality of retail hybrid seed, we used the experimental yield data and compared
yields across the three types of seed that were purchased and planted: farmer seed, authentic
hybrid seed and retail hybrid seed. The experimental yield data provide us with plot-specific
yields for different combinations of seed and fertilizer quality. To determine the quality
difference between authentic and retail hybrid seed, we estimate what mix of authentic hybrid
and farmer seed would generate the same distribution of yields as retail hybrid seed.
Specifically, we used the entire sample of seed across all levels of fertilizer, and
matched observations by site and nitrogen content of fertilizer applied. Each of these strata
contains six plots, two growing farmer seed, two growing retail hybrid seed and two growing
authentic hybrid seed, and we denote the average yield for each seed type across the two plots
in each stratum 𝑠𝑠 by 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠. We then construct a new variable that is the weighted
sum of the average maize yield on the plots growing farmer seed in stratum s and the average
maize yield on the plots growing authentic hybrid seed in stratum s: 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚 =
𝛼𝛼𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑚𝑚𝑠𝑠𝑓𝑓 + (1 − 𝛼𝛼)𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑓𝑓𝑎𝑎𝑡𝑡ℎ𝑠𝑠𝑒𝑒𝑡𝑡𝑚𝑚𝑒𝑒. We compare the distribution of this variable with the
distribution of yields generated by retail hybrid seed, 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑠𝑠,𝑓𝑓𝑠𝑠𝑡𝑡𝑓𝑓𝑚𝑚𝑟𝑟. We judge the two
distributions to be the same if the first four central moments are equal.
To estimate 𝛼𝛼 based on matching the mean (𝜇𝜇), variance (𝜎𝜎2), skewness (𝛾𝛾1) and
kurtosis (𝛾𝛾2) of the two distributions, we use the simulated method of moments (Gourieroux
and Montfort, 1996). Specifically, we define the vector 𝑮𝑮(𝛼𝛼), which contains the difference
in the first four simulated moments of the yield distribution generated by mixing farmer and
authentic hybrid seed with the ratio 𝛼𝛼:1-𝛼𝛼 and the yield distribution of retail hybrid seed
𝑮𝑮(𝛼𝛼) =
⎝
⎛
𝜇𝜇𝑚𝑚𝑚𝑚𝑚𝑚(𝛼𝛼) − 𝜇𝜇𝑓𝑓𝑠𝑠𝑡𝑡𝑓𝑓𝑚𝑚𝑟𝑟𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚2 (𝛼𝛼) − 𝜎𝜎𝑓𝑓𝑠𝑠𝑡𝑡𝑓𝑓𝑚𝑚𝑟𝑟2
𝛾𝛾1,𝑚𝑚𝑚𝑚𝑚𝑚(𝛼𝛼) − 𝛾𝛾1,𝑓𝑓𝑠𝑠𝑡𝑡𝑓𝑓𝑚𝑚𝑟𝑟𝛾𝛾2,𝑚𝑚𝑚𝑚𝑚𝑚(𝛼𝛼) − 𝛾𝛾2,𝑓𝑓𝑠𝑠𝑡𝑡𝑓𝑓𝑚𝑚𝑟𝑟⎠
⎞ .
(1)
We then solve for 𝛼𝛼 that minimizes the squared weighted sum of the moment conditions
𝛼𝛼� = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑌𝑌𝑎𝑎𝛼𝛼 𝑮𝑮(𝛼𝛼)′𝑾𝑾𝑮𝑮(𝛼𝛼) , (2)
where the weighting matrix 𝑾𝑾 is the inverse of the covariance matrix of the data moments,
which is obtained by bootstrapping the yield distribution 1,000 times.
A.4. Household survey
A household survey was administered at the end of the second season of 2013 to a sample of
farmers residing nearby the trading center visited as part of the 2014 fertilizer study (see
details above). Households were sampled using a two-stage sampling strategy. For each
trading center, a list of nearby villages (Local council 1) were assembled and villages within
a 5-kilometer radius from the trading center and 5–10 kilometer distance from the trading
center were identified. One village within a 5-kilometer radius from the trading center (strata
1) and one village 5–10 kilometer distance from the trading center (strata 2) were then
randomly picked. For the sampled villages, a list of households was collected from the Local
council chairman and 10 households were randomly picked from each strata. The sampled
farmers were asked for informed consent to participate in the survey. The respondent was the
head of the household if available at the time of the interview or the closest family member of
the household head. If neither could be found, or the household refused to participate, a
replacement household was chosen when possible (replacement rate less than 5%). The
objective of the survey was to collect detailed information from small-scale maize farmers on
their agricultural practices, including input use and market interactions, and their expectations
about the quality of and economic return to fertilizers. In total, information was collected
from 396 farmers of which 312 were smallholder farmers.1
In Section 5 (“The economic returns to technology”), we use the household survey
data to measure the price of maize and complementary expenses to adoption. The market
price of maize is derived by dividing the total value of the sale with the amount of maize
harvested and sold during the first season of 2013. Since the reported output price is strongly
left-skewed, we used the median rather than the mean price. Family labor is derived by
calculating the number of male and female adult full days (eight hours) of labor (seasonally
adjusted as data was collected for the last two months of a 5 months season). Expenses on
hired labor is the response to the question of how much did the household pay, including the
value of in-kind payments, for hired labor (seasonally adjusted as data was collected for the
last two months of a 5 months season).
Fertilizer use is use of inorganic fertilizer in 2013. Improved seeds use is use of
purchased (improved) seeds (OPV or hybrid) in 2013.
Household survey data was also used to derive expected maize yield (under three
different scenarios: (a) without using fertilizer; (b) by applying the recommended amount of
urea using fertilizer bought from the nearest shop; (c) by applying the recommended amount
of urea using fertilizer of the best official quality) and expected nutrient content of fertilizer
purchased from the nearest retail shop. To measure expected maize yield, the respondents
were first asked to give an estimate of the range of the distribution (i.e. highest and lowest
possible amount of dry maize in kilos that the farmer would expect to get). The enumerator
then calculated three evenly spaced mass points between the minimum and the maximum
stated by the farmer. For each elicitation, farmers were given 10 beans and instructed to place
the beans on a plate describing the chance that the event in question would be lower or equal
1 The FAO and the International Fund for Agricultural Development define small scale farmers as farmers with farms of two hectares or less (5 acres or less). We follow this definition here and also drop farmers with less than 0.5 acre (0.2 hectare).
than this number. Enumerators were asked to check farmers’ understanding in the sense that
the number of beans for the minimum value should always be zero, the number of beans for
the maximum value should always be 10 and to prompt respondents to ensure that answers
are non-decreasing. Respondents viewed by the enumerators as having “Very low
understanding” of the elicitation questions were dropped and the sample was trimmed for top
and bottom 1% of expected yield. We also collected data on farmers’ expectations of the
nitrogen content of fertilizers in the nearest local shop by asking the respondent to assess the
quality of fertilizer on a scale of 1 to 10, where 0 means there is no nitrogen, 5 means that
half of the official nitrogen is there, and 10 is the best possible quality. Finally, in section 7
we exploit farmers’ beliefs about nitrogen content (to measure prior beliefs) of fertilizers in
the nearest local shop by using the same belief elicitation method as described above.
Descriptive statistics for the household survey based variables we use are reported in
Table A4.
A.5. LSMS data and estimation of the residual and the CV
The Uganda National Panel Surveys (Uganda LSMS-ISA) contain four waves (2009-2010,
2010-2011, 2011-2012, and 2013-14) of household survey data from which plot specific
measures of yield, 𝑦𝑦𝑚𝑚𝑖𝑖(𝑡𝑡)𝑡𝑡, where subscript 𝑌𝑌 denotes household, 𝑗𝑗(𝑡𝑡) denotes the plot at time 𝑡𝑡
(season-year), can be derived for two seasons each in 2009, 2010, 2011, and 2013. Note that
the plot is time-variant. In each season, all farmers planting at least one plot of maize and
reporting the quantity for the maize harvested in kilograms of dry grain are included. The raw
yield data – estimated as metric tons of maize per hectare of land – include observations with
implausibly large yields and as a consequence the sample is trimmed for top 5% of yield.2
A.6. 2016 Follow-up study
A follow-up study was completed in May 2016. One of the objectives of the study was to
assess nutritional dilution of other types of fertilizers, specifically DAP – a multinutrient
fertilizer with nitrogen and phosphorus as the main nutrients. In the follow-up study we
followed a similar procedure as for the urea testing reported in section 3, but on a smaller
scale. Specifically, seven agro-retailer were sampled (one each from seven randomly sampled
2 The top 1% observations in the LSMS data vary between 39.5-5,148 metric tons per hectares (MT/ha), and the top 5% varies between 7.4-5,148 MT/ha. Maximum yield, using the experimental yield data, is 2.98 (when using traditional seeds and no fertilizer) and 7.4 MT/ha (when using authentic hybrid and authentic fertilizer).
districts) and three 2kg bags of fertilizer where bought each month for a total of 126 fertilizer
samples. We tested DAP for percent nitrogen (%N) content (should contain 18 percent
nitrogen) and percent phosphorus (%P) content (should contain 20 percent phosphorus). We
then calculate the rate of dilution as the weighted sum of dilution of nitrogen and phosphorus;
i.e., �1838� �18−%𝑁𝑁𝑗𝑗
18� + �20
38� �20−%𝑃𝑃𝑗𝑗
20�, where subscript 𝑗𝑗 refers to DAP sample 𝑗𝑗 and %𝑁𝑁𝑖𝑖 and
%𝑃𝑃𝑖𝑖 is percentage of nitrogen and phosphorus in sample 𝑗𝑗. The average rate of dilution of
DAP is 25.9%, ranging from essentially 0 to 91% dilution. See Table A3 for details.
A.7 Additional calculations
The willingness to pay with uncertainty to the realization of yields when adopting at scale is
∫ ∫𝜋𝜋(𝜃𝜃|𝜔𝜔1, . .𝜔𝜔𝑡𝑡)𝑎𝑎(𝜂𝜂)𝑢𝑢 �𝑝𝑝𝑚𝑚𝑎𝑎(𝜃𝜃) + 𝜂𝜂 − (1 + 𝑎𝑎)�𝑌𝑌ℎ + 𝑊𝑊𝑊𝑊𝑃𝑃(𝜃𝜃)��𝑌𝑌𝜃𝜃𝑌𝑌𝜂𝜂 −10 𝜓𝜓(𝑌𝑌𝑓𝑓) ≥
𝑢𝑢�𝑝𝑝𝑚𝑚𝑎𝑎(0)� − 𝜓𝜓(𝑌𝑌𝑓𝑓),
where 𝜂𝜂 is the shock to yield with density 𝑎𝑎(𝜂𝜂). In the simulations we take this shock to be
normally distributed with a standard deviation up to one half of the standard deviation we
estimate on the experimental plots.
The density of dilution level 𝜃𝜃 after experimenting for 𝑌𝑌 = 1 … 𝑡𝑡 rounds (or on 𝑡𝑡 plots)
and when 𝜃𝜃� varies each period (variant 2 of the model) is
𝜋𝜋(𝜃𝜃|𝜔𝜔1, … ,𝜔𝜔𝑡𝑡) =∏ 𝑓𝑓�𝜔𝜔𝑚𝑚�𝜃𝜃�𝑚𝑚��𝜃𝜃�𝑚𝑚 𝜋𝜋(𝜃𝜃)
∫ ∏ 𝑓𝑓�𝜔𝜔𝑚𝑚�𝜃𝜃�𝑚𝑚��𝜃𝜃�𝑚𝑚 𝜋𝜋(𝜃𝜃)𝑌𝑌𝜃𝜃10
.
A.8 Additional references
Gourieroux, C., and A. Montfort, Simulation-Based Econometric Methods (Oxford University Press, 1996).
Loveland, P. and J. Webb, “Is There a Critical Level of Organic Matter in the Agricultural Soils of Temperate Regions: a review”, Soil & Tillage Research 70 (2003), 1–18
B. Additional tables
Table A.1. Percent of households using fertilizer and improved seed varieties
(1) (2) (3) (4)
% of cultivating households using
any fertilizer
% of cultivating maize growing
households using fertilizer
% of cultivating households using any improved seeds
% of cultivating maize growing
households using any improved
seeds
Burkina Faso 45.0 (7,408)
61.1 (3,768)
18.5 (7,405)
27.8 (3,768)
Ethiopia 62.0 (3,167)
66.9 (1,826)
24.7 (3,066)
34.4 (1,826)
Malawi 78.4 (2,039)
80.7 (1,970)
- 48.7 (1,970)
Mali 45.2 (2,230)
65.0 (946)
28.0 (2,275)
34.3 (946)
Niger 21.1 (2,126)
- 14.7 (2,124)
-
Nigeria 41.9 (2,917)
49.7 (1,382)
- -
Tanzania 15.1 (3,061)
18.8 (2,066)
39.3 (2,769)
45.7 (2,066)
Uganda 6.6 (2,435)
9.0 (1,362)
21.9 (2,433)
26.9 (1,362)
Notes. Data from the 2014 Burkina Faso, the 2013/2014 Ethiopia, the 2013 Malawi, the 2014 Mali, the 2014 Niger, the 2012/2013 Nigeria, the 2012/2013 Tanzania, and the 2013/2014 Uganda LSMS-ISA. All summary statistics are weighted at the household level. Sample size in parenthesis. % of cultivating households using any fertilizer measures whether the household reports using inorganic fertilizer on at least one plot. % of cultivating maize growing households using fertilizer measures whether the household reports using inorganic fertilizer on at least one plot and also grows maize on at least one plot. % of cultivating households using any improved seeds measures whether the household reports using improved seeds on at least one plot. % of cultivating maize growing households using any improved seeds measures whether the household reports using improved seeds on at least one plot and also grows maize on at least one plot. No seed varietal characteristics are observed in Nigeria. Malawi report seed varieties conditional on type of crop (for some crops). Summary statistics for maize growing farmers in Niger is not reported due to small sample of maize farmers.
Table A.2. Estimates of the distribution of the noise in the signal equation
(1) (2) (3) (4) (5) (6) Uganda National Panel Surveys Agricultural trial Years Yield (𝑦𝑦�) 𝜎𝜎𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿/𝑦𝑦� Obs. Yield (𝑦𝑦�) 𝜎𝜎𝑠𝑠/𝑦𝑦� Plots 2009-2013 1.39
(1.34-1.45) 0.70 2,036 - - -
2009 1.30 (1.19-1.41)
0.52 606 - - -
2010 1.26 (1.16-1.35)
0.55 694 - - -
2011 1.64 (1.50-1.77)
0.32 393 - - -
2013 1.57 (1.43-1.70)
0.26 343 - - -
2014 - - - 1.82 (1.63-2.02)
0.29 30
Notes. Columns (1)-(3) use LSMS-ISA data for Uganda. Yield (𝑦𝑦�) is average maize yield (metric tons per hectare), with 95% CI in parenthesis. The standard deviation 𝜎𝜎𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 in the relative standard deviation of the residual, 𝜎𝜎𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿/𝑦𝑦�, is the standard deviation of the residual from a household fixed effects regression 𝑦𝑦𝑚𝑚𝑖𝑖(𝑡𝑡)𝑡𝑡 = 𝑠𝑠𝑌𝑌𝑠𝑠𝑌𝑌𝑚𝑚𝑖𝑖(𝑡𝑡)𝑡𝑡 + 𝛼𝛼𝑚𝑚 + 𝜖𝜖𝑚𝑚𝑖𝑖(𝑡𝑡)𝑡𝑡, where 𝑦𝑦𝑚𝑚𝑖𝑖(𝑡𝑡)𝑡𝑡 is maize yield (metric tons per hectare) for household 𝑌𝑌, on plot 𝑗𝑗(𝑡𝑡), in period 𝑡𝑡, 𝑠𝑠𝑌𝑌𝑠𝑠𝑌𝑌𝑚𝑚𝑖𝑖(𝑡𝑡)𝑡𝑡 is plot size in hectare, and 𝛼𝛼𝑚𝑚 are household fixed effects (see section A.5 for details). Sample selection: In each wave (four waves with yield data for 2009, 2010, 2011, and 2013, with two planting seasons per year), all farmers planting at least one plot of maize using traditional technologies (i.e. no improved seeds, no fertilizers, no pesticides, and no hired labor) and reporting the quantity for the maize harvested in kilograms of dry grain are included. As the data include observations with implausibly large yields, the sample is trimmed for top 5% of yield. Columns (4)-(6) use experimental yield data. Yield (𝑦𝑦�) is average maize yield with traditional inputs (no improved seeds and no fertilizers) with 95% CI in parenthesis. 𝜎𝜎𝑠𝑠 is the standard deviation of the residual from equation (8) using the experimental yield data and the relative standard deviation of the residual normalizes the standard deviation with average yield based on traditional seeds and no fertilizer.
Table A.3. Rate of dilution (%) of DAP retail fertilizers
Mean Standard deviation Minimum Maximum Observations
Dilution DAP (%) 25.8 27.2 0.3 91.1 126
Notes. The rate of dilution of sample 𝑗𝑗 is the weighted sum of dilution of nitrogen and phosphorus; i.e., �1838� �
18−%𝑁𝑁𝑗𝑗18
� + �2038� �
20−%𝑃𝑃𝑗𝑗20
�. See section A6 for details.
Table A.4. Descriptive statistics for the household survey based variables
Mean Median Std. dev. Min Max Obs
Market price maize 757 500 1293 7 15000 205 Expenses on hired labor 168.2 44.7 418.3 0 5648.1 310 Family labor days 113 96 111 0 1152 312 Using fertilizer 0.21 0 0.41 0 1 312 Using improved seeds 0.48 0 0.48 0 1 312 Expected yield no fertilizers 1.47 0.98 1.92 0.04 16.5 287 fertilizers from nearest shop 2.54 1.59 3.38 0.08 33.6 292 authentic fertilizer 5.28 2.24 33.3 0.11 568.1 291 Expected nitrogen content 28.4 27.6 8.0 4.6 46 295
Notes. See section A4 for details. 312 smallholder farmers were surveyed. Market price in Ugandan Shillings (UGX). Expenses on hired labor in ‘000 UGX. Family labor in days (8 hours/day). Expected yield in metric tons per hectare. Expected nitrogen content in percent Nitrogen.
C. Additional figures
Figure A.1. The yield distribution of retail hybrid seed and the simulated seed
The solid line represents the cumulative distribution of maize yields (metric tons per hectare) observed on the experimental plots when growing hybrid seed purchased from retailers. The dashed line represents the cumulative distribution of the simulated maize yield obtained when mixing farmer seed and authentic hybrid seed with the ratio 0.52:0.48.
Figure A.2. Rate of returns to technology adoption as a function of average yield
The solid line represents rate of returns to adoption of technologies available in local retail markets as a function of the % of baseline revenue (𝜑𝜑). The dashed line represents rate of returns to adoption of authentic technologies as a function of the % of baseline revenue (𝜑𝜑). See text for details.
0.2
.4.6
.81
Dist
ribut
ion
func
tion
1 2 3 4 5 6Yield (metric tons per hectare)
Retail hybrid seed Simulated mix
-50
050
100
150
Rate
of r
etur
n to
ado
ptio
n (%
)
60 80 100 120 140Percent of baseline revenue
Retail technologies Authentic technologies
Figure A.3. Willingness to pay: Adding uncertainty to the realization of yields when adopting at scale
The dashed line represents the average willingness to pay in the baseline model where each of the 𝑁𝑁 farmers in the household survey experiment for 5 periods with authentic fertilizer (see section 7.4.2.) The solid line represents the average willingness to pay when adding uncertainty to the realization of yields when adopting at scale (after 5 periods of experimentations). The additional yield shock (see section A7) is assumed to be normally distributed with a standard deviation varying from 0% to 80% of the standard deviation we estimate on the experimental plots.
Std dev. of the yield shock (𝜂𝜂) expressed in % of the std. dev. of noise in the signal equation (𝜎𝜎𝑠𝑠2)
Ave
rage
will
ingn
ess t
o pa
y
Figure A.4 Market for high quality
Panel A: Learning after 5 periods
Panel B: Share of farmers with a willingness to pay above the market price
Panel A: Log10 odds ratios in favor of profitable fertilizers after 5 periods when authentic fertilizers are supplied under three scenarios. Panel B: Share of farmers with a normalized willingness to pay above the market price (𝑊𝑊𝑊𝑊𝑃𝑃 > 1) when authentic fertilizers are supplied under three scenarios. Baseline scenario (solid line); 50% higher standard deviation than in the baseline scenario (dashed line); 50% lower standard deviation of than in the baseline scenario (dotted line).
Log10 Odds ratio in favor of profitability
Number of periods of experimentations
Dis
tribu
tion
func
tion
100% std. dev. Std. dev. 50% higher Std. dev. 50% lower
Shar
e of
farm
ers
100% std. dev. Std. dev. 50% higher Std. dev. 50% lower
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